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arXiv · 2609.07530

Geodesics for generalised Monge-Amp\`{e}re equations

Gao Chen·Kartick Ghosh·Sijie Nie
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Abstract

Xiuxiong Chen proved the existence of $C^{1, \bar 1}$ geodesics in the space of K\"{a}hler potentials and the convexity of the $J$-functional along $C^{1, \bar 1}$ geodesics. Analogous results were proved by Collins and Yau for the hypercritical Leung--Yau--Zaslow equation. In this paper, we study a similar picture for generalised Monge--Amp\`{e}re equations associated with two right-Noetherian polynomials in proper position.

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Gao Chen, Kartick Ghosh, Sijie Nie. 2026-09-07. Geodesics for generalised Monge-Amp\`{e}re equations. https://arxiv.org/abs/2609.07530

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