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Geodesics for generalised Monge-Ampère equations
Abstract
Xiuxiong Chen proved the existence of C1, 1̅ geodesics in the space of Kähler potentials and the convexity of the J-functional along C1, 1̅ 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--Ampère equations associated with two right-Noetherian polynomials in proper position.
Related
- The coerciveness and generalised Monge-Ampère equations
- Global C2,α estimate for complex Monge--Ampère equations on compact Kähler manifolds
- Solutions to Monge-Ampère Equations with Low Codimensional singularities
- Geometric Viewpoint of L∞ Estimates for Linearized Monge-Ampère Equations
- Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds
BibTeX
@misc{chen2026geodesics,
title = {{Geodesics for generalised Monge-Ampère equations}},
author = {Gao Chen and Kartick Ghosh and Sijie Nie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07530},
eprint = {2609.07530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07530},
}
RIS
TY - UNPB
TI - Geodesics for generalised Monge-Ampère equations
AU - Gao Chen
AU - Kartick Ghosh
AU - Sijie Nie
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.07530
UR - https://arxiv.org/abs/2609.07530
AB - Xiuxiong Chen proved the existence of C^1, 1̅ geodesics in the space of Kähler potentials and the convexity of the J-functional along C^1, 1̅ 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--Ampère equations associated with two right-Noetherian polynomials in proper position.
ER -