有限多点的Lipschitz推广

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2017-07-20 DOI:10.1515/agms-2018-0010

Giuliano Basso

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引用次数: 4

摘要

摘要我们考虑了拟度量空间中具有值的Lipschitz映射，并将这种映射推广到有限多个点。我们证明了在这种情况下，每个1-Lipschitz映射都允许一个扩展，使得它的Lipschitz-常数从上到下由加点数加1来定界。此外，我们证明了如果源空间是Hilbert空间，目标空间是Banach空间，那么存在一个扩展，使得它的Lipschitz常数从上到下由加总点加1的平方根定界。我们讨论度量变换的应用。

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Lipschitz Extensions to Finitely Many Points

Abstract We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by the number of added points plus one. Moreover, we prove that if the source space is a Hilbert space and the target space is a Banach space, then there exists an extension such that its Lipschitz constant is bounded from above by the square root of the total of added points plus one. We discuss applications to metric transforms.

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.