Universidad de Granada

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Showing 2014 · math.DGShow all

14 papers · 2 filters

math.DG2014

Constant mean curvature surfaces with boundary on a sphere

Rafael López, Juncheol Pyo

In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the b…

math.DG2014

Capillary surfaces of constant mean curvature in a right solid cylinder

Rafael López, Juncheol Pyo

In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the su…

math.DG2014★ 6 cited

Capillary surfaces in a cone

Rafael López, Juncheol Pyo

We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant ang…

math.DG2014★ 5 cited

Area-stationary and stable surfaces of class $C^{1}$ in the sub-Riemannian Heisenberg group $H^{1}$

Matteo Galli, Manuel Ritoré

We consider surfaces of class $C^{1}$ in the $3$ -dimensional sub-Riemannian Heisenberg group $H^{1}$ . Assuming the surface is area-stationary, i.e., a critical point of the s…

math.DG2014★ 15 cited

Embedded minimal surfaces in $R^{n}$

Antonio Alarcon, Franc Forstneric, Francisco J. Lopez

In this paper, we prove that every confomal minimal immersion of an open Riemann surface into $R^{n}$ for $n \geq 5$ can be approximated uniformly on compacts by conformal min…

math.DG2014★ 5 cited

Every conformal minimal surface in $R^{3}$ is isotopic to the real part of a holomorphic null curve

Antonio Alarcon, Franc Forstneric

In this paper, we show that for every conformal minimal immersion $u : M \to R^{3}$ from an open Riemann surface $M$ to $R^{3}$ there exists a smooth isotopy $u_t:M\to\m…

math.DG2014

Geometric barriers for the existence of hypersurfaces with prescribed curvatures in $M^{n} \times R$

José A. Gálvez, Victorino Lozano

We show the existence of a deformation process of hypersurfaces from a product space $M_{1} \times R$ into another product space $M_{2} \times R$ such that the relation of the principal…

math.DG2014★ 4 cited

On the topology of translating solitons of the mean curvature flow

Francisco Martin, Andreas Savas-Halilaj, Knut Smoczyk

In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.

math.DG2014

CMC foliations of closed manifolds

William H. Meeks, Joaquin Perez

We prove that every closed, smooth $n$ -manifold $X$ admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic i…

math.DG2014

Isoperimetric and stable sets for log-concave perturbations of Gaussian measures

César Rosales

Let $Ω$ be an open half-space or slab in $R^{n + 1}$ endowed with a perturbation of the Gaussian measure of the form $f (p) := exp (ω (p) - c ∣ p ∣^{2})$ , where $c > 0$ and $ω$ is a smoo…

math.DG2014★ 19 cited

A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products

Marie-Amelie Lawn, Miguel Ortega

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we descri…

math.DG2014★ 3 cited

The Dynamics Theorem for properly embedded minimal surfaces

William H. Meeks, Joaquín Pérez, Antonio Ros

In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) i…

math.DG2014★ 1 cited

Capillary surfaces inside polyhedral regions

Antonio Alarcon, Rabah Souam

In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is pres…

math.DG2014★ 2 cited

Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies

Manuel Ritoré, Efstratios Vernadakis

In this paper we consider the isoperimetric profile of convex cylinders $K \times R^{q}$ , where $K$ is an $m$ -dimensional convex body, and of cylindrically bounded convex sets…

Constant mean curvature surfaces with boundary on a sphere

Capillary surfaces of constant mean curvature in a right solid cylinder

Capillary surfaces in a cone

Area-stationary and stable surfaces of class C1 in the sub-Riemannian Heisenberg group H1

Embedded minimal surfaces in Rn

Every conformal minimal surface in R3 is isotopic to the real part of a holomorphic null curve

Geometric barriers for the existence of hypersurfaces with prescribed curvatures in Mn×R

On the topology of translating solitons of the mean curvature flow

CMC foliations of closed manifolds

Isoperimetric and stable sets for log-concave perturbations of Gaussian measures

A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products

The Dynamics Theorem for properly embedded minimal surfaces

Capillary surfaces inside polyhedral regions

Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies

Area-stationary and stable surfaces of class $C^{1}$ in the sub-Riemannian Heisenberg group $H^{1}$

Embedded minimal surfaces in $R^{n}$

Every conformal minimal surface in $R^{3}$ is isotopic to the real part of a holomorphic null curve

Geometric barriers for the existence of hypersurfaces with prescribed curvatures in $M^{n} \times R$