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Isoperimetric inequalities for submanifolds. Jellett–Minkowski's formula revisited
Author(s) -
Gimeno Vicent
Publication year - 2015
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdu053
Subject(s) - isoperimetric inequality , mathematics , submanifold , minkowski space , isoperimetric dimension , bounded function , boundary (topology) , mathematical analysis , pure mathematics , domain (mathematical analysis) , ambient space , space (punctuation) , geometry , linguistics , philosophy
In this paper, we provide an extension to the Jellett–Minkowski formula for immersed submanifolds within ambient manifolds which possess a pole and radial curvatures bounded from above or below. Using this generalized Jellett–Minkowski formula allows us to focus on several isoperimetric problems. Specifically, it becomes possible to concentrate on lower bounds for the isoperimetric quotients of any pre‐compact domain with a smooth boundary, or on the isoperimetric profile of the submanifold and its modified volume. In the particular case of a rotationally symmetric model space with strictly decreasing radial curvatures, an Aleksandrov‐type theorem is provided.