Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 304, pp. 434 - 493

We prove existence and uniqueness of solutions to the Minkowski problem in any domain of dependence D in (2+1)-dimensional Minkowski space, provided D is...

Minkowski space | Constant curvature surfaces | Mongeâ€“AmpÃ¨re equation | Universal TeichmÃ¼ller theory | MATHEMATICS | Monge-Ampere equation | HYPERSURFACES | GAUSS CURVATURE | Universal Teichmuller theory | Mathematics

Minkowski space | Constant curvature surfaces | Mongeâ€“AmpÃ¨re equation | Universal TeichmÃ¼ller theory | MATHEMATICS | Monge-Ampere equation | HYPERSURFACES | GAUSS CURVATURE | Universal Teichmuller theory | Mathematics

Journal Article

2011, Progress in mathematics, ISBN 9783034801447, Volume 290, xii, 166

This introduction to the subject of mean curvature flow of hypersurfaces has a special emphasis on the analysis of singularities and provides a detailed...

Global differential geometry | Curvature | Flows (Differentiable dynamical systems) | Mathematics | Differential equations, Parabolic

Global differential geometry | Curvature | Flows (Differentiable dynamical systems) | Mathematics | Differential equations, Parabolic

Book

JOURNAL OF GEOMETRIC ANALYSIS, ISSN 1050-6926, 10/2017, Volume 27, Issue 4, pp. 3071 - 3084

We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of typeM(n) (c) x R, whereM(n) (c) is a space form...

Constant mean curvature surfaces | SPACE | MATHEMATICS | SUBMANIFOLDS | HYPERSURFACES | Surfaces with parallelmean curvature | HOPF | Surfaces with finite total curvature

Constant mean curvature surfaces | SPACE | MATHEMATICS | SUBMANIFOLDS | HYPERSURFACES | Surfaces with parallelmean curvature | HOPF | Surfaces with finite total curvature

Journal Article

Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 2011, Volume 59, Issue 10, pp. 2103 - 2115

At small length scales, several size-effects in both physical phenomena and properties can be rationalized by invoking the concept of surface energy....

Nanostructures | Surface stress | Surface elasticity | Size-effects | Surface energy | PHYSICS, CONDENSED MATTER | CONSTANTS | NANO-INHOMOGENEITIES | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | TENSION | STRAIN-GRADIENT ELASTICITY | MECHANICS | FILMS | SOLIDS | METAL NANOWIRES | STRESS | GOLD NANOWIRES | Stress (Psychology) | Mechanical engineering | Force and energy | Surface chemistry | Nanocomposites | Communities | Mathematical analysis | Nanomaterials | Modulus of elasticity | Nanostructure | Curvature

Nanostructures | Surface stress | Surface elasticity | Size-effects | Surface energy | PHYSICS, CONDENSED MATTER | CONSTANTS | NANO-INHOMOGENEITIES | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | TENSION | STRAIN-GRADIENT ELASTICITY | MECHANICS | FILMS | SOLIDS | METAL NANOWIRES | STRESS | GOLD NANOWIRES | Stress (Psychology) | Mechanical engineering | Force and energy | Surface chemistry | Nanocomposites | Communities | Mathematical analysis | Nanomaterials | Modulus of elasticity | Nanostructure | Curvature

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2018, Volume 335, pp. 809 - 837

Given a closed flat 3-torus N, for each H>0 and each non-negative integer g, we obtain area estimates for closed surfaces with genus g and constant mean...

Curvature estimates | Area estimates | H-lamination | Minimal surface | Injectivity radius | Constant mean curvature | EXISTENCE | MINIMAL-SURFACES | H-SURFACES | GENUS | UNIQUENESS | EMBEDDED SURFACES | MATHEMATICS

Curvature estimates | Area estimates | H-lamination | Minimal surface | Injectivity radius | Constant mean curvature | EXISTENCE | MINIMAL-SURFACES | H-SURFACES | GENUS | UNIQUENESS | EMBEDDED SURFACES | MATHEMATICS

Journal Article

6.
Full Text
Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Physical Review Letters, ISSN 0031-9007, 02/2016, Volume 116, Issue 5, p. 056102

Surface tension is a macroscopic manifestation of the cohesion of matter, and its value sigma(infinity) is readily measured for a flat liquid-vapor interface....

PRESSURE | PHYSICS, MULTIDISCIPLINARY | NUCLEUS | HOMOGENEOUS NUCLEATION RATES | LENGTH | SIZE | CHAMBER | CONDENSATION | SYSTEMS | FREE-ENERGY | WATER | Models, Theoretical | Gases - chemistry | Surface Tension | Nucleation | Approximation | Mathematical analysis | Liquid-vapor interfaces | Constants | Surface tension | Mathematical models | Droplets | Physics - Chemical Physics | Engineering Sciences | Chemical Sciences | Physics

PRESSURE | PHYSICS, MULTIDISCIPLINARY | NUCLEUS | HOMOGENEOUS NUCLEATION RATES | LENGTH | SIZE | CHAMBER | CONDENSATION | SYSTEMS | FREE-ENERGY | WATER | Models, Theoretical | Gases - chemistry | Surface Tension | Nucleation | Approximation | Mathematical analysis | Liquid-vapor interfaces | Constants | Surface tension | Mathematical models | Droplets | Physics - Chemical Physics | Engineering Sciences | Chemical Sciences | Physics

Journal Article

ACM Transactions on Graphics (TOG), ISSN 0730-0301, 08/2012, Volume 31, Issue 4, pp. 1 - 11

We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture...

constant mean curvature | mesh quality | centroidal Voronoi tessellation | surface modeling | Surface modeling | Centroidal Voronoi tessellation | Constant mean curvature | Mesh quality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMAL-SURFACES | PARTIAL-DIFFERENTIAL-EQUATIONS | TENSION MEMBRANE STRUCTURES | COMPUTATION | DIAGRAM | CENTROIDAL VORONOI TESSELLATIONS | Asymptotic properties | Finite element method | Equivalence | Mathematical analysis | Evolution | Mathematical models | Curvature | Free boundaries

constant mean curvature | mesh quality | centroidal Voronoi tessellation | surface modeling | Surface modeling | Centroidal Voronoi tessellation | Constant mean curvature | Mesh quality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMAL-SURFACES | PARTIAL-DIFFERENTIAL-EQUATIONS | TENSION MEMBRANE STRUCTURES | COMPUTATION | DIAGRAM | CENTROIDAL VORONOI TESSELLATIONS | Asymptotic properties | Finite element method | Equivalence | Mathematical analysis | Evolution | Mathematical models | Curvature | Free boundaries

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2017, Volume 287, Issue 1, pp. 1 - 38

We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean $$C^{2}$$ C 2 -smooth surface in the Heisenberg...

Heisenberg group | Steiner formula | Riemannian approximation | Sub-Riemannian geometry | Secondary 53A35 | 52A39 | Mathematics, general | Primary 53C17 | Mathematics | Gaussâ€“Bonnet theorem | CONSTANT MEAN-CURVATURE | MINIMAL-SURFACES | CONVEXITY | Gauss-Bonnet theorem | FORMULA | MATHEMATICS | CARNOT GROUPS | HYPERSURFACES | GEOMETRY

Heisenberg group | Steiner formula | Riemannian approximation | Sub-Riemannian geometry | Secondary 53A35 | 52A39 | Mathematics, general | Primary 53C17 | Mathematics | Gaussâ€“Bonnet theorem | CONSTANT MEAN-CURVATURE | MINIMAL-SURFACES | CONVEXITY | Gauss-Bonnet theorem | FORMULA | MATHEMATICS | CARNOT GROUPS | HYPERSURFACES | GEOMETRY

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 8/2019, Volume 201, Issue 1, pp. 281 - 315

Let M be a globally hyperbolic maximal compact 3-dimensional spacetime locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well known that...

53C42 | 53C50 | Mathematics | Topology | Conical singularities | Lorentzian geometry | Constant curvature surfaces | Convex and Discrete Geometry | Teichmuller theory | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Differential Geometry | SPACETIMES | MATHEMATICS | POINT PARTICLES | SURFACES

53C42 | 53C50 | Mathematics | Topology | Conical singularities | Lorentzian geometry | Constant curvature surfaces | Convex and Discrete Geometry | Teichmuller theory | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Differential Geometry | SPACETIMES | MATHEMATICS | POINT PARTICLES | SURFACES

Journal Article

Nature Materials, ISSN 1476-1122, 05/2016, Volume 15, Issue 5, pp. 583 - 588

Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes....

CHEMISTRY, PHYSICAL | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | GEOMETRY | Constraints | Algorithms | Mathematical analysis | Flats | Programming | Constants | Curvature | Sheets

CHEMISTRY, PHYSICAL | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | GEOMETRY | Constraints | Algorithms | Mathematical analysis | Flats | Programming | Constants | Curvature | Sheets

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2018, Volume 265, Issue 9, pp. 4486 - 4529

We consider a symmetric restricted three-body problem on surfaces MÎº2 of constant Gaussian curvature Îºâ‰ 0, which can be reduced to the cases Îº=Â±1. This problem...

KAM tori | Hamiltonian formulation | The restricted three body problem | Surfaces of constant curvature | Periodic solutions | Averaging theory | MATHEMATICS | SPACES | SINGULARITIES | INTRINSIC APPROACH | RELATIVE EQUILIBRIA

KAM tori | Hamiltonian formulation | The restricted three body problem | Surfaces of constant curvature | Periodic solutions | Averaging theory | MATHEMATICS | SPACES | SINGULARITIES | INTRINSIC APPROACH | RELATIVE EQUILIBRIA

Journal Article

General Relativity and Gravitation, ISSN 0001-7701, 9/2018, Volume 50, Issue 9, pp. 1 - 7

In this note we present a result establishing the existence of a compact CMC Cauchy surface from a curvature condition related to the strong energy condition.

Cosmological spacetime | Constant mean curvature | Theoretical, Mathematical and Computational Physics | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Curvature condition | Physics | Astronomy, Astrophysics and Cosmology | LORENTZ | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

Cosmological spacetime | Constant mean curvature | Theoretical, Mathematical and Computational Physics | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Curvature condition | Physics | Astronomy, Astrophysics and Cosmology | LORENTZ | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2013, Volume 46, Issue 29, pp. 295202 - 20

A close-packed organization with circular symmetry of a large number of small discs on a plane is obtained when the centres of the discs are distributed...

PACKING | SYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SPIRAL LATTICES | Grain boundaries | Isotropy | Discs | Planes | Mathematical analysis | Organizations | Disks | Constants | Curvature

PACKING | SYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SPIRAL LATTICES | Grain boundaries | Isotropy | Discs | Planes | Mathematical analysis | Organizations | Disks | Constants | Curvature

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2015, Volume 285, pp. 980 - 1024

Given a complex surface X with singularities of class T and no nontrivial holomorphic vector field, endowed with a KÃ¤hler class Î©0, we consider smoothings...

Smoothing singular constant scalar curvature KÃ¤hler surfaces and minimal Lagrangians | MATHEMATICS | DEL PEZZO SURFACES | BLOWING-UP | MANIFOLDS | DEFORMATIONS

Smoothing singular constant scalar curvature KÃ¤hler surfaces and minimal Lagrangians | MATHEMATICS | DEL PEZZO SURFACES | BLOWING-UP | MANIFOLDS | DEFORMATIONS

Journal Article

The Journal of Chemical Physics, ISSN 0021-9606, 11/2017, Volume 147, Issue 18, p. 184112

To investigate how the curvature of a reactive surface can affect reaction kinetics, we use a simple model in which a diffusion-limited bimolecular reaction...

PROTEIN ASSOCIATION | BURIED ACTIVE-SITE | KINETICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | REACTIVITY | CHEMISTRY, PHYSICAL | CONTROLLED LIGAND-BINDING | ROTATIONAL DIFFUSION | BROWNIAN DYNAMICS | CELL-BOUND RECEPTORS | ORIENTATION CONSTRAINTS | RATE-CONSTANT | Finite element method | Surface reactions | Reaction kinetics | Mathematical models | Diffusion | Curvature | Linear functions

PROTEIN ASSOCIATION | BURIED ACTIVE-SITE | KINETICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | REACTIVITY | CHEMISTRY, PHYSICAL | CONTROLLED LIGAND-BINDING | ROTATIONAL DIFFUSION | BROWNIAN DYNAMICS | CELL-BOUND RECEPTORS | ORIENTATION CONSTRAINTS | RATE-CONSTANT | Finite element method | Surface reactions | Reaction kinetics | Mathematical models | Diffusion | Curvature | Linear functions

Journal Article

Journal of Colloid And Interface Science, ISSN 0021-9797, 2007, Volume 314, Issue 1, pp. 184 - 198

The interface shape separating a gas layer within a superhydrophobic surface consisting of a square lattice of posts from a pressurized liquid above the...

Overall force balance | Lagrangian evolution equation | Constant mean curvature surface | Static contact line | Superhydrophobic surface | Pressure stability | Interfacial shape | superhydrophobic surface | WETTABILITY | PARALLEL CYLINDERS | overall force balance | DRAG REDUCTION | static contact line | CHEMISTRY, PHYSICAL | CAPILLARY PHENOMENA | EFFECTIVE SLIP | MICROCHANNELS | constant mean curvature surface | interfacial shape | ASSEMBLIES | WATER-REPELLENT SURFACES | pressure stability | ULTRAHYDROPHOBIC SURFACES | ROUGH SURFACES

Overall force balance | Lagrangian evolution equation | Constant mean curvature surface | Static contact line | Superhydrophobic surface | Pressure stability | Interfacial shape | superhydrophobic surface | WETTABILITY | PARALLEL CYLINDERS | overall force balance | DRAG REDUCTION | static contact line | CHEMISTRY, PHYSICAL | CAPILLARY PHENOMENA | EFFECTIVE SLIP | MICROCHANNELS | constant mean curvature surface | interfacial shape | ASSEMBLIES | WATER-REPELLENT SURFACES | pressure stability | ULTRAHYDROPHOBIC SURFACES | ROUGH SURFACES

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 7/2019, Volume 56, Issue 1, pp. 57 - 86

In this paper, we prove that stable, compact without boundary, oriented, nonzero constant mean curvature surfaces in the de Sitterâ€“Schwarzschild and...

Geometry | 53C42 | 53A10 | Stability | Mathematical Physics | Constant mean curvature | Analysis | Global Analysis and Analysis on Manifolds | Warped product manifolds | Mathematics | Differential Geometry | 49Q10 | MATHEMATICS | Lower bounds | Euclidean geometry | Submerging | Euclidean space | Fields (mathematics) | Surface stability | Dimensional stability | Manifolds (mathematics) | Curvature | Mathematics - Differential Geometry

Geometry | 53C42 | 53A10 | Stability | Mathematical Physics | Constant mean curvature | Analysis | Global Analysis and Analysis on Manifolds | Warped product manifolds | Mathematics | Differential Geometry | 49Q10 | MATHEMATICS | Lower bounds | Euclidean geometry | Submerging | Euclidean space | Fields (mathematics) | Surface stability | Dimensional stability | Manifolds (mathematics) | Curvature | Mathematics - Differential Geometry

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 10/2017, Volume 27, Issue 4, pp. 3441 - 3473

We obtain area growth estimates for constant mean curvature graphs in E(kappa, tau)-spaces with k <= 0, by finding sharp upper bounds for the volume of...

Area estimates | Heisenberg group | Homogeneous 3-manifolds | Minimal surfaces | Constant mean curvature | Height estimates | MINIMAL GRAPHS | MINKOWSKI SPACE | X R | MATHEMATICS | HYPERSURFACES | UNBOUNDED-DOMAINS | MANIFOLDS | SURFACE EQUATION | Mathematics - Differential Geometry

Area estimates | Heisenberg group | Homogeneous 3-manifolds | Minimal surfaces | Constant mean curvature | Height estimates | MINIMAL GRAPHS | MINKOWSKI SPACE | X R | MATHEMATICS | HYPERSURFACES | UNBOUNDED-DOMAINS | MANIFOLDS | SURFACE EQUATION | Mathematics - Differential Geometry

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2015, Volume 164, Issue 14, pp. 2643 - 2722

For all N >= 9, we find smooth entire epigraphs in R-N, namely, smooth domains of the form Omega := {x is an element of R-N broken vertical bar X-N broken...

MATHEMATICS | SYMMETRY | PHASE-TRANSITIONS | HYPERSURFACES | GIORGI | ELLIPTIC-EQUATIONS | INDEX | DOMAINS | EMBEDDED MINIMAL-SURFACES | RIEMANNIAN-MANIFOLDS | CONJECTURE

MATHEMATICS | SYMMETRY | PHASE-TRANSITIONS | HYPERSURFACES | GIORGI | ELLIPTIC-EQUATIONS | INDEX | DOMAINS | EMBEDDED MINIMAL-SURFACES | RIEMANNIAN-MANIFOLDS | CONJECTURE

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 12/2015, Volume 129, pp. 143 - 159

The minimal surface theory in Finsler geometry deserves to be well developed as that in Riemannian geometry. In this paper, we derive the mean curvature of...

Finsler geometry | Finsler sphere | Minimal surface | Berger sphere | [formula omitted]-curvature | S-curvature | ROTATION | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | METRICS | ALPHA | Killing | Energy use | Minimal surfaces | Mathematical analysis | Images | Constants | Manifolds (mathematics) | Invariants

Finsler geometry | Finsler sphere | Minimal surface | Berger sphere | [formula omitted]-curvature | S-curvature | ROTATION | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | METRICS | ALPHA | Killing | Energy use | Minimal surfaces | Mathematical analysis | Images | Constants | Manifolds (mathematics) | Invariants

Journal Article

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