Advances in Mathematics, ISSN 0001-8708, 08/2019, Volume 352, pp. 133 - 157

Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We...

Curvature estimates | Sheeting theorems | Weak stability | Constant mean curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | REGULARITY | STABILITY | INDEX | MINIMAL HYPERSURFACES | SURFACES

Curvature estimates | Sheeting theorems | Weak stability | Constant mean curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | REGULARITY | STABILITY | INDEX | MINIMAL HYPERSURFACES | SURFACES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2015, Volume 425, Issue 1, pp. 588 - 609

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in Sn×R and Hn×R. When these surfaces do not lie in Sn or Hn and they...

Surfaces with constant mean curvature | Biconservative surfaces

Surfaces with constant mean curvature | Biconservative surfaces

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 10/2019, Volume 187, pp. 125 - 133

Given a compact manifold with boundary M of dimension m≥3 and a nondegenerate Riemannian metric g∗ having null scalar curvature, constant mean curvature, and...

The Yamabe problem | Constant mean curvature | Uniqueness of solutions | Riemannian metrics | Flat scalar curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | THEOREM | SCALAR-FLAT METRICS | BIFURCATION | Manifolds (mathematics) | Curvature

The Yamabe problem | Constant mean curvature | Uniqueness of solutions | Riemannian metrics | Flat scalar curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | THEOREM | SCALAR-FLAT METRICS | BIFURCATION | Manifolds (mathematics) | Curvature

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 13, pp. 4626 - 4637

Let M be a Riemannian three-manifold of nonnegative Ricci curvature, Ric >= 0. Suppose that M is conformally flat and simply connected or more generally that...

MATHEMATICS | CONSTANT MEAN-CURVATURE

MATHEMATICS | CONSTANT MEAN-CURVATURE

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 11/2013, Volume 65, Issue 4, pp. 1345 - 1362

We study the intrinsic and the extrinsic geometry of Clifford tori in Berger spheres S-3, tau > 0, and use these results to prove several local rigidity and...

MATHEMATICS | CONSTANT MEAN-CURVATURE

MATHEMATICS | CONSTANT MEAN-CURVATURE

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2018, Volume 264, Issue 11, pp. 6994 - 7005

We introduce a method, based on the Poincaré–Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in...

MATHEMATICS | CONSTANT MEAN-CURVATURE | SYMMETRY | HYPERSURFACES | PLANE | CONJECTURE

MATHEMATICS | CONSTANT MEAN-CURVATURE | SYMMETRY | HYPERSURFACES | PLANE | CONJECTURE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2019, Volume 372, Issue 8, pp. 5483 - 5506

There exists a holomorphic quadratic differential defined on any H-surface immersed in the homogeneous space {\mathbb{E}(\kappa , \tau )} given by U. Abresch...

Constant mean curvature surfaces | Simons' equation | CONSTANT MEAN-CURVATURE | 1ST STABILITY EIGENVALUE | eigenvalue estimate | pinching theorem | MATHEMATICS | Codazzi pairs | HYPERSURFACES | finite total curvature | S-2 X R | homogeneous space | SURFACES

Constant mean curvature surfaces | Simons' equation | CONSTANT MEAN-CURVATURE | 1ST STABILITY EIGENVALUE | eigenvalue estimate | pinching theorem | MATHEMATICS | Codazzi pairs | HYPERSURFACES | finite total curvature | S-2 X R | homogeneous space | SURFACES

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 280, Issue 1, pp. 1 - 15

Let Sigma be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in Rn+1. Suppose that Sigma meets those two hyperplanes in...

Constant mean curvature | Stable | Capillary surface | DROPS | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONTACT | capillary surface | stable | STABILITY | constant mean curvature | BOUNDARY | SURFACES

Constant mean curvature | Stable | Capillary surface | DROPS | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONTACT | capillary surface | stable | STABILITY | constant mean curvature | BOUNDARY | SURFACES

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 05/2015, Volume 425, Issue 1, pp. 588 - 609

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in S-n x R and H-n x R. When these surfaces do not lie in S-n or H-n...

MATHEMATICS | CONSTANT MEAN-CURVATURE | TENSOR | MATHEMATICS, APPLIED | SUBMANIFOLDS | Surfaces with constant mean curvature | THEOREM | HYPERSURFACES | SPACE-FORMS | Biconservative surfaces | FINITE TOTAL CURVATURE | RIEMANNIAN-MANIFOLDS

MATHEMATICS | CONSTANT MEAN-CURVATURE | TENSOR | MATHEMATICS, APPLIED | SUBMANIFOLDS | Surfaces with constant mean curvature | THEOREM | HYPERSURFACES | SPACE-FORMS | Biconservative surfaces | FINITE TOTAL CURVATURE | RIEMANNIAN-MANIFOLDS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2010, Volume 362, Issue 6, pp. 2845 - 2857

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1072 - 1086

In this paper, we investigate the critical points of solutions to the prescribed constant mean curvature equation with Neumann and Robin boundary conditions...

Prescribed constant mean curvature equation | Non-degeneracy | Critical point | Uniqueness | Forests and forestry

Prescribed constant mean curvature equation | Non-degeneracy | Critical point | Uniqueness | Forests and forestry

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 09/2018, Volume 35, Issue 19, p. 195005

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 11/2016, Volume 140, Issue 8, pp. 901 - 907

In this note we characterize compact hypersurfaces of dimension n≥2 with constant mean curvature H immersed in space forms of constant curvature and satisfying...

Constant mean curvature hypersurfaces | Rigidity | MATHEMATICS, APPLIED | hypersurfaces | Constant mean curvature | TORI | SPHERES | CONJECTURE

Constant mean curvature hypersurfaces | Rigidity | MATHEMATICS, APPLIED | hypersurfaces | Constant mean curvature | TORI | SPHERES | CONJECTURE

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 04/2019, Volume 112, Issue 4, pp. 437 - 445

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2017, Volume 317, pp. 553 - 574

We generalize Meeks and Yau's embeddedness result on the solutions of the Plateau problem to constant mean curvature disks. We show that any minimizing H-disk...

Embeddedness | H-surfaces | Minimal surfaces | H-disks | H-Plateau problem | Constant mean curvature | EXISTENCE | TOPOLOGY | CONSTANT MEAN-CURVATURE | UNIQUENESS | MATHEMATICS | AREA | DEHN LEMMA | MANIFOLDS | SURFACES

Embeddedness | H-surfaces | Minimal surfaces | H-disks | H-Plateau problem | Constant mean curvature | EXISTENCE | TOPOLOGY | CONSTANT MEAN-CURVATURE | UNIQUENESS | MATHEMATICS | AREA | DEHN LEMMA | MANIFOLDS | SURFACES

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 02/2019, Volume 62, pp. 72 - 82

In this work we complete a classification of pseudo-parallel hypersurfaces of Sn×R and Hn×R, that was partially given by F. Lin and B. Yang. As an application,...

Pseudo-symmetric | Hypersurface | Pseudo-parallel | Constant mean curvature | Minimal

Pseudo-symmetric | Hypersurface | Pseudo-parallel | Constant mean curvature | Minimal

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 12/2015, Volume 269, Issue 12, pp. 3812 - 3867

In 1996, Huisken–Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean...

Foliation by surfaces of constant mean curvature | Asymptotically flat | Linear momentum | CMC-foliation | CONSTANT MEAN-CURVATURE | FOLIATIONS | BEHAVIOR | INFINITY | MATHEMATICS | MASS | SYSTEMS | MANIFOLDS | STABLE SPHERES | SURFACES

Foliation by surfaces of constant mean curvature | Asymptotically flat | Linear momentum | CMC-foliation | CONSTANT MEAN-CURVATURE | FOLIATIONS | BEHAVIOR | INFINITY | MATHEMATICS | MASS | SYSTEMS | MANIFOLDS | STABLE SPHERES | SURFACES

Journal Article

JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 10/2013, Volume 255, Issue 7, pp. 1828 - 1838

We present a deformation process of surfaces from a product space M-1 x R into another product space M-2 x R such that the relation of the principal curvatures...

MATHEMATICS | DIRICHLET PROBLEM | CONSTANT MEAN-CURVATURE | GRAPHS

MATHEMATICS | DIRICHLET PROBLEM | CONSTANT MEAN-CURVATURE | GRAPHS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 371, Issue 2, pp. 1253 - 1269

We show that for any \mathcal {C}^0 Jordan curve \Gamma in S^2_{\infty }(\mathbf {H}^3), there exists an embedded H-plane \mathcal {P}_H in \mathbf {H}^3 with...

EXISTENCE | SPACE | MATHEMATICS | CONSTANT MEAN-CURVATURE | PLATEAU PROBLEM | HYPERSURFACES | SURFACES

EXISTENCE | SPACE | MATHEMATICS | CONSTANT MEAN-CURVATURE | PLATEAU PROBLEM | HYPERSURFACES | SURFACES

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 02/2018, Volume 56, pp. 295 - 307

We deal with complete constant mean curvature spacelike hypersurfaces immersed in a Lorentzian space form and satisfying a suitable Okumura type inequality,...

Lorentzian space forms | Constant mean curvature | Okumura type inequality | Hyperbolic cylinders | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | DESITTER SPACE | SITTER SPACE

Lorentzian space forms | Constant mean curvature | Okumura type inequality | Hyperbolic cylinders | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | DESITTER SPACE | SITTER SPACE

Journal Article

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