2 citations · 6 across the 10 of their papers we have counts for
10 papers
Power Convexity of Solutions to the Complex Monge-Ampère Equation in Complex Dimension Two
Hongyu Chen, Jingchen Hu, Li Sheng
In this paper, we establish the power convexity of solutions to the complex Monge-Ampère equation in a convex set in the complex 2 dimensional Euclidean…
Convexity of the Potential Function of the Einstein-Kähler Metric on a Convex Domain
Jingchen Hu, Li Sheng
Suppose that u is the potential function of a complete Kähler-Einstein metric on a bounded strictly convex domain in . We prove that u itself is strictly convex.
A Maximum Rank Theorem for Solutions to the Homogenous Complex Monge-Ampère Equation in a -Convex Ring
Jingchen Hu
Suppose are two bounded strongly -convex domains in , with and . Let $\mathcal{R}=Ω_1\backslash\overline{Ω_0…
The Preservation of Convexity by Geodesics in the Space of Kähler Potentials on Complex Affine Manifolds
Jingchen Hu
On a compact complex affine manifold with a constant coefficient Kähler metric , we introduce a concept: -convexity and show that -convexity is preserved by…
A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials
Jingchen Hu
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-Ampère equation. As…
Loss of Regularity of Solutions to Shock Reflection Problems by a Non-symmetric Convex Wedge with Potential Flow Equations
Jingchen Hu
In this paper, we study the problem of shock reflection by a wedge, with the potential flow equation, which is a simplification of the Euler System. In the work of M. Feldman and G…
An Obstacle for Higher Regularity of Geodesics in the Space of Kähler Potentials
Jingchen Hu
In this paper we address the following question regarding the regularity of geodesics in the space of Kähler potentials. Given a geodesic which is highly regular, and has smooth bo…
Geodesic Convexity of Small Neighborhood in the Space of Kähler Potentials
Xiuxiong Chen, Mikhail Feldman, Jingchen Hu
We show that, given , , any point in space of non-degenerate smooth Kähler potentials has a small neighborhood with respect to norm…
Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow
Gui-Qiang Chen, Mikhail Feldman, Jingchen Hu +1
We are concerned with the suitability of the main models of compressible fluid dynamics for the Lighthill problem for shock diffraction by a convex corned wedge, by studying the re…
Gradient estimate of a Neumann eigenfunction on a compact manifold with boundary
Jingchen Hu, Yiqian Shi, Bin Xu
Let be a Neumann eigenfunction with respect to the positive Laplacian on a compact Riemannian manifold with boundary such that in the interior of…