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arXiv · 2102.05277

Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: $\epsilon$-geodesics

Long Li
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Abstract

The purpose of this article is to study the strict convexity of the Mabuchi functional along a $C^{1,1}$-geodesic, with the aid of the $\epsilon$-geodesics. We proved the $L^2$-convergence of the fiberwise volume element of the $\epsilon$-geodesic. Moreover, the geodesic is proved to be uniformly fiberwise non-degenerate if the Mabuchi functional is $\epsilon$-affine.

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Long Li. 2021-02-10. Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: $\epsilon$-geodesics. https://arxiv.org/abs/2102.05277

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