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ON THE REGULARITY OF SETS IN RIEMANNIAN MANIFOLDS

Part of: Existence theories Calculus on manifolds; nonlinear operators

Published online by Cambridge University Press:  18 March 2020

A. SEPAHVAND  and
A. BARANI
A. SEPAHVAND
Affiliation:
Department of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, Iran
A. BARANI*
Affiliation:
Department of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, Iran e-mail: sepahvand.ami@fs.lu.ac.ir
*
e-mail: barani.a@lu.ac.ir
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Abstract

This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Fréchet and proximal subdifferentials of the distance function from a closed subset in a Riemannian manifold are represented by corresponding normal cones of the set.

Keywords

normal conenormal regularitysubdifferential regularitytangential regularitydirectional regularityRiemannian manifold

MSC classification

Primary: 49J53: Set-valued and variational analysis
Secondary: 58C20: Differentiation theory (Gateaux, Fréchet, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 110 , Issue 3 , June 2021 , pp. 386 - 405
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by W. Moors

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