Existence and convexity for hyperspheres of prescribed mean curvature

Andrejs Treibergs

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Closed hypersurfaces of $S^{4}$ with two constant symmetric curvatures

Sebastião Carneiro de Almeida, Fabiano Gustavo Braga Brito (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

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A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature H, for some r = 1, ..., n.

Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of $ℝ^{n + 1}$ and $ℍ^{n + 1}$

Barbara Nelli, Harold Rosenberg (1997)

Annales de l'institut Fourier

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We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic $n$ -dimensional space and we obtain removable singularities theorems.

Convexity estimates for flows by powers of the mean curvature

Felix Schulze (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the evolution of a closed, convex hypersurface in $ℝ^{n + 1}$ in direction of its normal vector, where the speed equals a power $k \geq 1$ of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to $1$ , depending only on $k$ and $n$ , then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere. ...

On a problem of W. J. Firey in connection with the characterization of spheres.

Leichtweiss, Kurt (1995)

Mathematica Pannonica

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A logarithmic Gauss curvature flow and the Minkowski problem

Kai-Seng Chou, Xu-Jia Wang (2000)

Annales de l'I.H.P. Analyse non linéaire

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Interior curvature estimates for hypersurfaces of prescribed mean curvature

Klaus Ecker, Gerhard Huisken (1989)

Annales de l'I.H.P. Analyse non linéaire

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Displaying similar documents to “Existence and convexity for hyperspheres of prescribed mean curvature”

Closed hypersurfaces of S 4 with two constant symmetric curvatures

Compact hypersurfaces with constant higher order mean curvatures.

Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of ℝ n + 1 and ℍ n + 1

Convexity estimates for flows by powers of the mean curvature

On a problem of W. J. Firey in connection with the characterization of spheres.

A logarithmic Gauss curvature flow and the Minkowski problem

Interior curvature estimates for hypersurfaces of prescribed mean curvature

Closed hypersurfaces of $S^{4}$ with two constant symmetric curvatures

Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of $ℝ^{n + 1}$ and $ℍ^{n + 1}$