Communications in Mathematical Physics, ISSN 0010-3616, 6/2017, Volume 352, Issue 2, pp. 703 - 718

We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MINIMAL-SURFACES | QUASI-LOCAL MASS | PHYSICS, MATHEMATICAL | COMPACT MANIFOLDS

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MINIMAL-SURFACES | QUASI-LOCAL MASS | PHYSICS, MATHEMATICAL | COMPACT MANIFOLDS

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

1984, 5th ed., ISBN 9780914098072, xv, 412

Book

2003, Translations of mathematical monographs, ISBN 9780821834794, Volume 221, x, 142

Book

DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 11/2019, Volume 168, Issue 16, pp. 3057 - 3102

We derive extrinsic curvature estimates for compact disks embedded in R-3 with nonzero constant mean curvature.

SPACE | MATHEMATICS | MULTIVALUED GRAPHS | THEOREM | DISKS | 3-MANIFOLDS | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

SPACE | MATHEMATICS | MULTIVALUED GRAPHS | THEOREM | DISKS | 3-MANIFOLDS | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

Journal Article

Annals of Mathematics, ISSN 0003-486X, 3/2012, Volume 175, Issue 2, pp. 755 - 833

It has long been conjectured that starting at a generic smooth closed embedded surface in R 3 , the mean curvature flow remains smooth until it arrives at a...

Tangents | Varifolds | Critical points | Hypersurfaces | Eigenvalues | Eigenfunctions | Polynomials | Mathematics | Entropy | Curvature | SPACE | MATHEMATICS | REGULARITY | THEOREM | SHAPES | CONSTRUCTION | MONOTONICITY | SELF-SIMILAR SURFACES | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

Tangents | Varifolds | Critical points | Hypersurfaces | Eigenvalues | Eigenfunctions | Polynomials | Mathematics | Entropy | Curvature | SPACE | MATHEMATICS | REGULARITY | THEOREM | SHAPES | CONSTRUCTION | MONOTONICITY | SELF-SIMILAR SURFACES | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

Journal Article

2012, University lecture series, ISBN 9780821869123, Volume 60., x, 182

Book

1992, ISBN 9780821825365, Volume no. 478., vi, 77

Book

2011, Graduate studies in mathematics, ISBN 0821853236, Volume 121, xii, 313

"Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in...

Minimal surfaces

Minimal surfaces

Book

Soft Matter, ISSN 1744-683X, 2018, Volume 14, Issue 12, pp. 2281 - 2294

Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is...

SCISSION | POLYMER SCIENCE | MODULUS | PHYSICS, MULTIDISCIPLINARY | SHAPE TRANSFORMATIONS | VESICLES | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | TENSION | LIPID-MEMBRANES | MECHANICS | BIOGENESIS | FISSION | PROTEINS | Helmholtz equations | Minimal surfaces | Mathematical analysis | Skewed distributions | Gaussian distribution | Boundary conditions | Neck | Curvature | Lipid bilayers | Membrane proteins

SCISSION | POLYMER SCIENCE | MODULUS | PHYSICS, MULTIDISCIPLINARY | SHAPE TRANSFORMATIONS | VESICLES | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | TENSION | LIPID-MEMBRANES | MECHANICS | BIOGENESIS | FISSION | PROTEINS | Helmholtz equations | Minimal surfaces | Mathematical analysis | Skewed distributions | Gaussian distribution | Boundary conditions | Neck | Curvature | Lipid bilayers | Membrane proteins

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

Geometric and Functional Analysis, ISSN 1016-443X, 6/2018, Volume 28, Issue 3, pp. 645 - 726

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as...

Analysis | Mathematics | MATHEMATICS | MINIMAL-SURFACES | MANIFOLDS | RIGIDITY | DIRAC

Analysis | Mathematics | MATHEMATICS | MINIMAL-SURFACES | MANIFOLDS | RIGIDITY | DIRAC

Journal Article

Journal of Mathematical Imaging and Vision, ISSN 0924-9907, 7/2018, Volume 60, Issue 6, pp. 784 - 815

We introduce numerical schemes for computing distances and shortest paths with respect to several planar paths models, featuring curvature penalization and...

Mathematical Methods in Physics | Euler–Mumford elastica | Dubins car | Voronoi reduction of quadratic forms | Signal,Image and Speech Processing | Hamilton–Jacobi equation | Viscosity solution | Computer Science | Image Processing and Computer Vision | Reeds–Shepp car | Applications of Mathematics | Fast-marching algorithm | STENCILS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | Reeds-Shepp car | Euler-Mumford elastica | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIFFUSION TENSOR | DISCRETIZATION | REDUCTION | ACTIVE CONTOURS | GLOBAL MINIMUM | SURFACES | GEOMETRY | Algorithms | Image processing | Anisotropy | Methods | Mathematics | Optimization and Control | Numerical Analysis | Analysis of PDEs

Mathematical Methods in Physics | Euler–Mumford elastica | Dubins car | Voronoi reduction of quadratic forms | Signal,Image and Speech Processing | Hamilton–Jacobi equation | Viscosity solution | Computer Science | Image Processing and Computer Vision | Reeds–Shepp car | Applications of Mathematics | Fast-marching algorithm | STENCILS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | Reeds-Shepp car | Euler-Mumford elastica | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIFFUSION TENSOR | DISCRETIZATION | REDUCTION | ACTIVE CONTOURS | GLOBAL MINIMUM | SURFACES | GEOMETRY | Algorithms | Image processing | Anisotropy | Methods | Mathematics | Optimization and Control | Numerical Analysis | Analysis of PDEs

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 06/2019, Volume 72, Issue 6, pp. 1231 - 1242

We show that a Riemannian 3‐manifold with nonnegative scalar curvature is flat if it contains an area‐minimizing cylinder. This scalar‐curvature analogue of...

MATHEMATICS | MATHEMATICS, APPLIED | MINIMAL-SURFACES | RIGIDITY | MASS | 3-MANIFOLDS | 2-SPHERES | Mathematics - Differential Geometry

MATHEMATICS | MATHEMATICS, APPLIED | MINIMAL-SURFACES | RIGIDITY | MASS | 3-MANIFOLDS | 2-SPHERES | Mathematics - Differential Geometry

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 07/2014, Volume 35, Issue 7-9, pp. 793 - 815

We consider a nonlocal (or fractional) curvature and we investigate similarities and differences with respect to the classical local case. In particular, we...

Nonlocal directional curvature | Fractional perimeters | Nonlocal mean curvature | Fractional Laplacian | s-minimal surfaces | MATHEMATICS, APPLIED | MINIMAL-SURFACES | LIMITING ARGUMENTS | Analogies | Asymptotic properties | Mathematical analysis | Nonlinearity | Functional analysis | Curvature | Optimization | Convergence

Nonlocal directional curvature | Fractional perimeters | Nonlocal mean curvature | Fractional Laplacian | s-minimal surfaces | MATHEMATICS, APPLIED | MINIMAL-SURFACES | LIMITING ARGUMENTS | Analogies | Asymptotic properties | Mathematical analysis | Nonlinearity | Functional analysis | Curvature | Optimization | Convergence

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2018, Volume 93, Issue 1, pp. 55 - 69

Let $M$ be a compact Riemannian manifold of nonnegative Ricci curvature and $\Sigma$ a compact embedded 2-sided minimal hypersurface in $M$. It is proved that...

Differential geometry | Ricci curvature | Minimal surface | Fundamental group | MATHEMATICS | minimal surface | fundamental group | MINIMAL-SURFACES | THEOREM | 3-MANIFOLDS | GEOMETRY

Differential geometry | Ricci curvature | Minimal surface | Fundamental group | MATHEMATICS | minimal surface | fundamental group | MINIMAL-SURFACES | THEOREM | 3-MANIFOLDS | GEOMETRY

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2018, Volume 146, Issue 6, pp. 2637 - 2646

In this paper we consider the evolution of boundaries of sets by a fractional mean curvature flow. We show that for any dimension n\geqslant 2, there exist...

And phrases | Fractional mean curvature flow | Fractional perimeter | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | fractional mean curvature flow | REGULARITY | NONLOCAL MINIMAL-SURFACES | PLANE-CURVES

And phrases | Fractional mean curvature flow | Fractional perimeter | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | fractional mean curvature flow | REGULARITY | NONLOCAL MINIMAL-SURFACES | PLANE-CURVES

Journal Article

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

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

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

IEEE Transactions on Circuits and Systems for Video Technology, ISSN 1051-8215, 08/2019, Volume 29, Issue 8, pp. 2205 - 2214

Ill-posed problems are very common in many image processing and computer vision tasks. To solve such problems, a regularization must be imposed. In this paper,...

Geometry | Computer vision | minimal surface | Image processing | Computational modeling | prior | regularization | Mathematical model | Task analysis | Mean curvature | Surface treatment | image processing | ENGINEERING, ELECTRICAL & ELECTRONIC

Geometry | Computer vision | minimal surface | Image processing | Computational modeling | prior | regularization | Mathematical model | Task analysis | Mean curvature | Surface treatment | image processing | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

The Journal of Physical Chemistry B, ISSN 1520-6106, 12/2017, Volume 121, Issue 50, pp. 11399 - 11409

I report for the first time an X-ray crystallographic study on single-crystal regions of cubic phases of a lyotropic liquid crystal. The single-crystal regions...

MEMBRANE-FUSION | TRANSFORMATION | IPMS BASED PHASES | DIAMOND | RECONSTRUCTION | BEHAVIOR | CHEMISTRY, PHYSICAL | HEXAGONAL PHASE | POLYMORPHISM | WATER SYSTEMS | PERIODIC MINIMAL-SURFACES | X-ray crystallography | Lipid membranes | Usage | Analysis | Gaussian processes | Research | Structure | Liquid crystals

MEMBRANE-FUSION | TRANSFORMATION | IPMS BASED PHASES | DIAMOND | RECONSTRUCTION | BEHAVIOR | CHEMISTRY, PHYSICAL | HEXAGONAL PHASE | POLYMORPHISM | WATER SYSTEMS | PERIODIC MINIMAL-SURFACES | X-ray crystallography | Lipid membranes | Usage | Analysis | Gaussian processes | Research | Structure | Liquid crystals

Journal Article

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