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arXiv · 2305.09932

Volume functionals on pseudoconvex hypersurfaces

Simon Donaldson·Fabian Lehmann
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Abstract

We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and discuss possible analogues of the affine isoperimetric inequality. In the last section of the paper we explore infinite dimensional aspects, including moment maps for diffeomorphism group actions.

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Simon Donaldson, Fabian Lehmann. 2023-05-17. Volume functionals on pseudoconvex hypersurfaces. https://arxiv.org/abs/2305.09932

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