Geometric Holder estimates for complex Monge-Ampere equations
Abstract
This paper is the continuation of our earlier work on Holder estimates for Kahler potentials on compact normal Kahler spaces. We establish a geometric counterpart for analytic Holder regularity of Kolodziej. If a singular metric ωϕ has Holder continuous potentials with respect to a smooth background metric, then its distance function is Holder continuous with respect to a smooth background distance. The result holds on normal Kahler spaces and yields compactness of the metric completion as well as its identification with the underlying complex space if ωϕ is a Kahler current. Under this positivity assumption, our estimates establish the Holder equivalence between the intrinsic canonical Kahler metrics and the extrinsic smooth metrics on Kahler-RCD spaces, particularly on smoothable Kahler-Einstein spaces.
Related
- Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization
- Geometric Viewpoint of L∞ Estimates for Linearized Monge-Ampère Equations
- Uniform estimates for complex Monge-Ampère equations II: Hermitian manifolds
- Geometric stability for complex Monge-Ampere equations
- Boundary Hölder Regularity of a Class of Monge–Ampère Equations at Some Special Points
BibTeX
@misc{guo2026geometric,
title = {{Geometric Holder estimates for complex Monge-Ampere equations}},
author = {Bin Guo and Jian Song and Jacob Sturm},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28982},
eprint = {2609.28982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28982},
}
RIS
TY - UNPB
TI - Geometric Holder estimates for complex Monge-Ampere equations
AU - Bin Guo
AU - Jian Song
AU - Jacob Sturm
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28982
UR - https://arxiv.org/abs/2609.28982
AB - This paper is the continuation of our earlier work on Holder estimates for Kahler potentials on compact normal Kahler spaces. We establish a geometric counterpart for analytic Holder regularity of Kolodziej. If a singular metric ω_ϕ has Holder continuous potentials with respect to a smooth background metric, then its distance function is Holder continuous with respect to a smooth background distance. The result holds on normal Kahler spaces and yields compactness of the metric completion as well as its identification with the underlying complex space if ω_ϕ is a Kahler current. Under this positivity assumption, our estimates establish the Holder equivalence between the intrinsic canonical Kahler metrics and the extrinsic smooth metrics on Kahler-RCD spaces, particularly on smoothable Kahler-Einstein spaces.
ER -