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arXiv · 1306.2478

Jellett-Minkowski's formula revisited. Isoperimetric inequalities for submanifolds in an ambient manifold with bounded curvature

Vicent Gimeno
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Abstract

In this paper we provide an extension to the Jellett-Minkowski's formula for immersed submanifolds into ambient manifolds which possesses a pole and radial curvatures bounded from above or below by the radial sectional curvatures of a rotationally symmetric model space. Using this Jellett-Minkowski's generalized formula we can focus on several isoperimetric problems. More precisely, on lower bounds for isoperimetric quotients of any precompact domain with smooth boundary, or on the isoperimetric profile of the submanifold and its modified volume. In the particular case of a model space with strictly decreasing radial curvatures, an Aleksandrov type theorem is provided.

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Vicent Gimeno. 2013-10-21. Jellett-Minkowski's formula revisited. Isoperimetric inequalities for submanifolds in an ambient manifold with bounded curvature. https://arxiv.org/abs/1306.2478

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