The isometry groups of riemannian manifolds admitting strictly convex functions

Takao Yamaguchi

Displaying similar documents to “The isometry groups of riemannian manifolds admitting strictly convex functions”

Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.

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We show how an operation of inf-convolution can be used to approximate convex functions with C smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.

A generalization of Berger's rigidity theorem for positively curved manifolds

Detlef Gromoll, Karsten Grove (1987)

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p-convex Riemannian manifolds.

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Norbert Kleinjohann (1981)

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Plateau-Stein manifolds

Misha Gromov (2014)

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We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.