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Is quasi-concavity preserved by heat flow?

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Abstract.

We investigate on the preservation of spatial quasi-concavity of the initial datum by the solutions of the heat equation and we give negative results in dimension N ≥ 2.

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Authors and Affiliations

  1. Mathematical Institute Tohoku University Aoba, Sendai, 980-8578, Japan

    Kazuhiro Ishige

  2. Dipartimento di Matematica ‘U. Dini’ Viale Morgagni 67/A, 50137, Firenze, Italy

    Paolo Salani

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  1. Kazuhiro Ishige
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  2. Paolo Salani
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Correspondence to Kazuhiro Ishige.

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Received: 11 May 2007

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Ishige, K., Salani, P. Is quasi-concavity preserved by heat flow?. Arch. Math. 90, 450–460 (2008). https://doi.org/10.1007/s00013-008-2437-y

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  • DOI: https://doi.org/10.1007/s00013-008-2437-y

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