4 papers
math.AP2022
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…
math.AP2021
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…
math.AP2018
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…
math.AP2018
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…