Paper · Mar 26, 2026
Regularity of solutions to Monge–Ampère equations on compact Hermitian manifolds
As on arXiv
Abstract
We study the stability and Hölder continuity of solutions to degenerate complex Monge–Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern–Ricci flow.
Comments: 22 pages. Comments are welcome!
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Singularities of the Chern-Ricci flow
Topics Generalized & G₂ flows, Kähler geometry · Same author Quang-Tuan Dang · Shared terms “Ampère equation”, “compact Hermitian”, “Hermitian manifolds”
-
Pluripotential Chern-Ricci Flows
Topics Generalized & G₂ flows, Kähler geometry, Stability & uniqueness · Same author Quang-Tuan Dang · Shared terms “compact Hermitian”, “Hermitian manifolds”, “Ampère equation”
-
The behavior of the second Ricci flow on complex parallelizable manifolds
Topics Generalized & G₂ flows · Shared terms “compact Hermitian”, “Hermitian manifolds”, “Chern”
-
Hermitian null loci
Topics Generalized & G₂ flows · Same author Quang-Tuan Dang · Shared terms “Hermitian”, “Chern”
-
On the Calabi estimate of geometric flows of Hermitian metrics
Topics Generalized & G₂ flows, Kähler geometry · Shared terms “Hermitian”, “Chern”
-
Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions
Topics Ricci flow · Shared terms “Hermitian manifolds”, “Ampère equation”, “Monge”
-
Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow
Topics Generalized & G₂ flows, Kähler geometry, Stability & uniqueness · Shared terms “Hermitian”, “Chern”, “reference”
-
The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds
Topics Generalized & G₂ flows, Kähler geometry · Shared terms “Ampère equation”, “Monge”, “Chern”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 10A.12Curve Shortening and Minimal Discs
How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.
- 11A.1The Equation and Its First Solutions
A heat equation for the metric: spheres, cylinders and scaling.