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On a class of graphs with perscribed mean curvature.

Duong Minh Duc, I.M.C. Salavessa (1994)

Manuscripta mathematica

On a conjecture about the Gauss map of complete spacelike surfaces with constant mean curvature in the Lorentz-Minkowski space.

Chaves, Rosa M.B., Cueva Cândido, Cláudia (2004)

Beiträge zur Algebra und Geometrie

On a free boundary problem for minimal surfaces.

M. Struwe (1984)

Inventiones mathematicae

On a sub-supersolution method for the prescribed mean curvature problem

Vy Khoi Le (2008)

Czechoslovak Mathematical Journal

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

On a system of partial differential equations in Heisenberg space. (Sur un système d'équations aux d'érivées partielles dans l'espace de Heisenberg.)

Bekkar, M. (2001)

Rendiconti del Seminario Matematico

On algebraic-geometrical parametrization of the constant mean curvature tori

Р.Ф. Бикбаев (1994)

Zapiski naucnych seminarov POMI

On asymptotic properties of maximal tubes and bands in a neighborhood of an isolated singularity in Minkowski space.

Klyachin, V.A. (2002)

Sibirskij Matematicheskij Zhurnal

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

On Deszcz symmetries of Wintgen ideal submanifolds

Miroslava Petrović-Torgašev, Leopold C. A. Verstraelen (2008)

Archivum Mathematicum

It was conjectured in [26] that, for all submanifolds $M^{n}$ of all real space forms ${\tilde{M}}^{n + m} (c)$ , the Wintgen inequality $ρ \leq H^{2} - ρ^{⊥} + c$ is valid at all points of $M$ , whereby $ρ$ is the normalised scalar curvature of the Riemannian manifold $M$ and $H^{2}$ , respectively $ρ^{⊥}$ , are the squared mean curvature and the normalised scalar normal curvature of the submanifold $M$ in the ambient space $\tilde{M}$ , and this conjecture was shown there to be true whenever codimension $m = 2$ . For a given Riemannian manifold $M$ , this inequality can be interpreted as follows:...