Closed geodesics with Lipschitz obstacle (Q1290973)
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scientific article; zbMATH DE number 1295278
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closed geodesics with Lipschitz obstacle |
scientific article; zbMATH DE number 1295278 |
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Closed geodesics with Lipschitz obstacle (English)
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6 October 1999
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It is considered a different kind of nonsmooth subset of \(\mathbb{R}^n\) with Lipschitz boundary. A new definition for geodesics on a general subset of \(\mathbb{R}^n\) is proposed and their basic property is showed. This definition is related to the nonsmooth critical point theory, presented below. The main result of this paper is a proof of the existence of at least one nonconstant closed geodesic in certain situations.
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Lipschitz obstacle
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nonsmooth subset
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nonsmooth critical point theory
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closed geodesic
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