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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
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
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
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
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 08/2012, Volume 31, Issue 4, pp. 1 - 11
Journal Article
Tohoku Mathematical Journal, ISSN 0040-8735, 09/2018, Volume 70, Issue 3, pp. 475 - 485
We explicitly determine tori that have a parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. 
Parallel mean curvature vector | Constant mean curvature surfaces in complex space forms | MATHEMATICS | constant mean curvature surfaces in complex space forms | MINIMAL-SURFACES | TOTALLY-REAL SUBMANIFOLDS | TERMS | CLASSIFICATION | X R | VECTOR
Journal Article
General Relativity and Gravitation, ISSN 0001-7701, 9/2019, Volume 51, Issue 9, pp. 1 - 14
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 7/2018, Volume 172, Issue 2, pp. 458 - 476
We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from ($$\text {n}+1$$ n+1... 
Volume preserving mean curvature flow | Submanifold | Constant mean curvature surface | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Effective dynamic | Quantum Physics | Adiabatic dynamic | Physics | Mean curvature flow | Statistical Physics and Dynamical Systems | SPHERES | STABILITY | LIMIT | PHYSICS, MATHEMATICAL | MOTION | CONVERGENCE | MAP
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 05/2018, Volume 110, Issue 5, pp. 523 - 531
We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to... 
Einstein submanifolds | Parallel mean curvature | Flat normal bundle | Principal normals | MATHEMATICS | SPACES | CONSTANT CURVATURE | ISOMETRIC IMMERSIONS
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 10/2019, Volume 144, pp. 121 - 125
We show that ruled real hypersurfaces with constant mean curvature in the complex projective and hyperbolic spaces must be minimal. This provides their... 
Minimal hypersurface | Complex hyperbolic space | Constant mean curvature | Complex space form | Complex projective space | Ruled hypersurface | MATHEMATICS | SUBMANIFOLDS | PHYSICS, MATHEMATICAL | REAL HYPERSURFACES
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 7/2019, Volume 56, Issue 1, pp. 57 - 86
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 12/2019, Volume 29, Issue 4, pp. 3293 - 3307
In this paper, we provide under certain geometric and physical assumptions new uniqueness and non-existence results for complete spacelike hypersurfaces of... 
53C42 | 53C50 | Mathematics | Abstract Harmonic Analysis | Spacelike hypersurface | Fourier Analysis | Constant mean curvature | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | 53C80 | Generalized Robertson–Walker spacetime
Journal Article
Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, 06/2017, Volume 48, Issue 2, pp. 187 - 198
In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice. 
Entire graph | Constant mean curvature | Killing graph | Unbounded region | MATHEMATICS
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 Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2015, Volume 22, Issue 5, pp. 1047 - 1066
The Hardy–Sobolev trace inequality can be obtained via harmonic extensions on the half-space of the Stein and Weiss weighted Hardy–Littlewood–Sobolev... 
Weighted trace Sobolev inequality | 35J60 | Analysis | Mathematics | 35B40 | Hardy–Sobolev inequality | Mean curvature | MATHEMATICS, APPLIED | EXPONENTS | SYMMETRY | CRITICAL GROWTH | CONSTANT | Hardy-Sobolev inequality | ELLIPTIC-EQUATIONS | BOUNDARY SINGULARITIES | RIEMANNIAN-MANIFOLDS | Equality
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 11/2018, Volume 133, pp. 91 - 101
A 3-dimensional Riemannian manifold is called Killing submersion if it admits a Riemannian submersion over a surface such that its fibers are the trajectories... 
Constant mean curvature | Killing submersions | Biharmonic surfaces | MATHEMATICS | PHYSICS, MATHEMATICAL | RIEMANNIAN-MANIFOLDS | Mathematics - Differential Geometry
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2014, Volume 271, Issue 1, pp. 213 - 230
We compute a Simons-type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several... 
Stress-energy tensor | Constant mean curvature | Biharmonic maps | MATHEMATICS | constant mean curvature | MAPS | biharmonic maps | stress-energy tensor | Mathematics - Differential Geometry
Journal Article
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