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Sechseckgewebe auf Flachen Positiver oder Negativer Krummung

Georg Stamou (1979)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Self-intersection Points in classical area-minimizing surfaces.

Claire C. Chan (1995)

Manuscripta mathematica

Sharp eigenvalue estimates of closed $H$ -hypersurfaces in locally symmetric spaces

Eudes L. de Lima, Henrique F. de Lima, Fábio R. dos Santos, Marco A. L. Velásquez (2019)

Czechoslovak Mathematical Journal

The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.

Simons Type Equation in $𝕊^{2} \times ℝ$ and $ℍ^{2} \times ℝ$ and Applications

Márcio Henrique Batista da Silva (2011)

Annales de l’institut Fourier

Let $Σ^{2}$ be an immersed surface in $M^{2} (c) \times ℝ$ with constant mean curvature. We consider the traceless Weingarten operator $φ$ associated to the second fundamental form of the surface, and we introduce a tensor $S$ , related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both $φ$ and $S$ . By using these equations, we characterize some immersions for which $| φ |$ or $| S |$ is appropriately bounded.

Size-minimizing rectifiable currents.

Frank Morgan (1989)

Inventiones mathematicae

SO(2) invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces.

Renzo Caddeo, Paola Piu, Andrea Ratto (1995)

Manuscripta mathematica

Solutions positives d'équations elliptiques non linéaires avec exposant de Sobolev critique et conjecture de Rellich pour les surfaces à courbure moyenne prescrite

H. Brezis (1982/1983)

Séminaire Équations aux dérivées partielles (Polytechnique)

Solutions to the mean curvature equation by fixed point methods.

Mariani, M.C., Rial, D.F. (1997)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Some contributions to the differential geometry of submanifolds [Book]

Barbara Opozda (1992)

Some existence and uniqueness theorems for doubly periodic minimal surfaces.

Fusheng Wei (1992)

Inventiones mathematicae

Some recent developments in the theory of properly embedded minimal surfaces in $ℝ^{3}$

Harold Rosenberg (1991/1992)

Séminaire Bourbaki

Some remarkable properties of $H$ -graphs.

Finn, Robert, Lu, Jianan (1997)

Memoirs on Differential Equations and Mathematical Physics

Some Results on Finiteness in Plateau's Problem, Part I.

Michael Beeson (1980)

Mathematische Zeitschrift

Some Results on Finiteness in Plateau's Problem, Part II.

Michael Beeson (1982)

Mathematische Zeitschrift

Some uniqueness and nonexistence theorems for embedded minimal surfaces.

Joaquín Pérez, Antonio Ros (1993)

Mathematische Annalen

Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

Georgi Ganchev, Vesselka Mihova (2013)

Open Mathematics

On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten surfaces...

Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes

Benoît Daniel (2009/2010)

Séminaire de théorie spectrale et géométrie

Nous passons en revue certains résultats récents sur l’existence et l’unicité des sphères à courbure moyenne constante dans les variétés riemanniennes homogènes simplement connexes de dimension $3$ et leurs liens avec le problème isopérimétrique dans ces variétés.

Currently displaying 1 – 20 of 41