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Erschienen in:
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2023 | OriginalPaper | Buchkapitel

9. Relative Isoperimetric Inequalities

verfasst von : Manuel Ritoré

Erschienen in: Isoperimetric Inequalities in Riemannian Manifolds

Verlag: Springer International Publishing

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Abstract

In this chapter, isoperimetric inequalities on domains with smooth boundary in complete Riemannian manifolds are considered. The perimeter here is the one relative to the domain \(\Omega \). If a smooth interface S separates \(\Omega \) into two sets, the relative perimeter of each one of these sets is the area of the interface. This means that there are no contributions to the relative perimeter coming from pieces in \(\partial \Omega \). While many of the techniques are adapted from the boundaryless case, some subtle differences appear. The geometry of the boundary, in particular its second fundamental form, will play a determinant role.

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Vorheriges Kapitel Isoperimetric Comparison for Sectional Curvature
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Metadaten
Titel
Relative Isoperimetric Inequalities
verfasst von
Manuel Ritoré
Copyright-Jahr
2023
Buch
Isoperimetric Inequalities in Riemannian Manifolds

Print ISBN: 978-3-031-37900-0

Electronic ISBN: 978-3-031-37901-7

Copyright-Jahr: 2023

DOI
https://doi.org/10.1007/978-3-031-37901-7_9

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