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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 | Monge–Ampère equation | Universal Teichmüller 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
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
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 2011, Volume 59, Issue 10, pp. 2103 - 2115
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
Journal Article
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
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 08/2012, Volume 31, Issue 4, pp. 1 - 11
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 | Gauss–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
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
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 Mκ2 of constant Gaussian curvature κ≠0, which can be reduced to the cases κ=±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
Journal Article
General Relativity and Gravitation, ISSN 0001-7701, 9/2018, Volume 50, Issue 9, pp. 1 - 7
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
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 Kähler class Ω0, we consider smoothings... 
Smoothing singular constant scalar curvature Kähler 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
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 7/2019, Volume 56, Issue 1, pp. 57 - 86
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
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
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
Journal Article
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