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arXiv · 2208.13651

A Metric Lower Bound Estimate for Geodesics in the Space of K\"ahler Potentials

Jingchen Hu
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Abstract

In this paper we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge-Amp\`ere equation. As a consequence, we find that in the space of K\"ahler potentials any two points close to each other in $C^2$ norm can be connected by a geodesic along which the associated metrics do not degenerate.

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Jingchen Hu. 2022-08-29. A Metric Lower Bound Estimate for Geodesics in the Space of K\"ahler Potentials. https://doi.org/10.1007/s12220-024-01654-1

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