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Finiteness Principles for Smooth Selection

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall Washington Road, Princeton, NJ, 08544, USA

    Charles Fefferman

  2. Department of Mathematics, The University of Texas at Austin, 2515 Speedway Stop C1200, Austin, TX, 78712-1202, USA

    Arie Israel

  3. Department of Mathematics, University of California, Davis, One Shields Ave, Davis, CA, 95616, USA

    Garving K. Luli

Authors
  1. Charles Fefferman
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  2. Arie Israel
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  3. Garving K. Luli
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Correspondence to Garving K. Luli.

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Fefferman, C., Israel, A. & Luli, G.K. Finiteness Principles for Smooth Selection. Geom. Funct. Anal. 26, 422–477 (2016). https://doi.org/10.1007/s00039-016-0366-7

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  • DOI: https://doi.org/10.1007/s00039-016-0366-7

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