Finiteness Principles for Smooth Selection

Charles Fefferman; Arie Israel; Garving K. Luli

doi:10.1007/s00039-016-0366-7

Finiteness Principles for Smooth Selection

Charles Fefferman, Arie Israel, Garving K. Luli

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

In this paper we prove finiteness principles for C^m(Rⁿ, R^D) and C^m ^- ¹ ^, ¹(Rⁿ, R^D) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is X= Rⁿ.

Original language	English (US)
Pages (from-to)	422-477
Number of pages	56
Journal	Geometric and Functional Analysis
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s00039-016-0366-7
State	Published - Apr 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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title = "Finiteness Principles for Smooth Selection",

abstract = "In this paper we prove finiteness principles for Cm(Rn, RD) and Cm - 1 , 1(Rn, RD) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is X= Rn.",

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AU - Luli, Garving K.

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N2 - In this paper we prove finiteness principles for Cm(Rn, RD) and Cm - 1 , 1(Rn, RD) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is X= Rn.

AB - In this paper we prove finiteness principles for Cm(Rn, RD) and Cm - 1 , 1(Rn, RD) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is X= Rn.

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Finiteness Principles for Smooth Selection

Abstract

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