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arXiv · 1408.2624

An integral formula in Kahler geometry with applications

Xiaodong Wang
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Abstract

We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedded hypersurface of constant mean curvature must be a geodesic sphere, provided the hypersurface is Hopf. A similar result is established on the complex projective space.

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Xiaodong Wang. 2014-08-12. An integral formula in Kahler geometry with applications. https://arxiv.org/abs/1408.2624

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