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