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We give an overview of semiconcavity, starting from the standard notion up to more recent generalizations in a different geometrical context, such as Carnot groups, focusing in particular on the viscosity characterization by bounds for second derivatives. We then apply these theories to show some recent results obtained by the author, in collaboration with Qing Liu and Ye Zhang. In particular, we show that the square Carnot-Carathéodory distance is h-semiconcave in step 2 Carnot groups.

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Semiconcavity, Viscosity Solutions and the Square Distance in Carnot Groups

  • 会议论文

  • 发表日期：

    2025年

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  • Federica Dragoni

摘要

We give an overview of semiconcavity, starting from the standard notion up to more recent generalizations in a different geometrical context, such as Carnot groups, focusing in particular on the viscosity characterization by bounds for second derivatives. We then apply these theories to show some recent results obtained by the author, in collaboration with Qing Liu and Ye Zhang. In particular, we show that the square Carnot-Carathéodory distance is h-semiconcave in step 2 Carnot groups.