Weiyong He

We will discuss the well-known isotopy problem in symplectic geometry in dimension four. Given a compact symplectic four manifold with a fixed symplectic class, a long standing problem is to ask whether all symplectic forms in the cohomology class...

Donaldson introduced a metric and a geometric structure on the space of volume forms on any compact Rimannian manifold. The geodesic equation is a degenerate fully nonlinear elliptic equation. Also this equation is relevant to many interesting...

The Calabi flow is a fourth order nonlinear parabolic flow, introduced by Calabi in 1980s, and it aims to find Kahler metrics with constant scalar curvature (or more generally extremal Kahler metrics). We prove that the Calabi flow can have a unique...

Recently Xiuxiong Chen and Jingrui Cheng have made a breakthrough on the existence of constant scalar curvature metrics on compact Kahler metrics, in view of Calabi-Donaldson program and Yau-Tian-Donaldson conjecture. The essential new input is a...

We study the existence and regularity of harmonic and biharmonic almost complex structures. Harmonic almost complex structures were introduced by C. Wood in 1990s. Since then there are considerate interest. For harmonic almost complex structure, we...