Prescribing the Mean Curvature

Vladimir Rovenski; Paweł Walczak

doi:10.1007/978-3-030-70067-6_3

Prescribing the Mean Curvature

Vladimir Rovenski
, Paweł Walczak

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter provides conditions either necessary or sufficient for a given quantity (either a scalar function or a vector field) to be the mean curvature of a given foliation with respect to some Riemannian metric. The particular case of this quantity being identically zero (tautness) has been described separately. In the codimension-one case, the only obstructions for a scalar function to be the mean curvature of a foliation arise from Stokes’ Theorem and a well known formula by H. Rummler relating mean curvature with the exterior derivative of the leaf volume form.

Original language	English
Title of host publication	Progress in Mathematics
Publisher	Birkhauser
Pages	123-151
Number of pages	29
DOIs	https://doi.org/10.1007/978-3-030-70067-6_3
State	Published - 2021

Publication series

Name	Progress in Mathematics
Volume	339
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

Access to Document

10.1007/978-3-030-70067-6_3

Cite this

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Prescribing the Mean Curvature

Abstract

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