304 Citations
Compact K\"ahler manifolds with positive orthogonal bisectional curvature
- Mathematics
- 2017
In this short note, using Siu-Yau's method [14], we give a new proof that any n-dimensional compact Kahler manifold with positive orthogonal bisectional curvature must be biholomorphic to…
Ricci flow on Kähler-Einstein manifolds
- Mathematics
- 2006
This is the continuation of our earlier article [10]. For any Kähler-Einstein surfaces with positive scalar curvature, if the initial metric has positive bisectional curvature, then we have proved…
Harmonic maps from Riemann surfaces into complex Finsler manifolds
- Mathematics
- 2015
Given a smooth map from a compact Riemann surface to a complex manifold equipped with a strongly pseudoconvex complex Finsler metric, we define the $\bar{\partial}$-energy of the map, whose absolute…
Minimal surfaces - variational theory and applications
- Mathematics
- 2014
Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by…
On quadratic orthogonal bisectional curvature
- Mathematics
- 2011
In this article we study compact K\ahler manifolds satisfying a certain nonnegativity condition on the bisectional curvature. Under this condition, we show that the scalar curvature is nonnegative…
Nonnegatively curved contact manifolds
- Mathematics
- 1986
A compact simply connected contact Riemannian manifold with positive sectional curvature is homeomorphic with a sphere if its contact structure is normal and regular. In dimension 3 the regularity…
Structure of Manifolds with Positive Curvature Based on Geometric Analysis
- Mathematics
- 2013
The Gauss-Bonnet theorem and the Cohn-Vossen inequality show that the only complete surface with positive curvature is either the sphere, RP, or the plane. In higher dimension, the curvature tensor…
HARMONIC MAP FLOW WITH LOW ∂̄-ENERGY
- Mathematics
- 2020
Let Σ be a compact oriented surface and N a compact Kähler manifold with nonnegative holomorphic bisectional curvature. For harmonic map flow starting from a map Σ → N with low ∂̄-energy, the limit…
Harmonic map flow with low $\bar{\partial}$-energy
- Mathematics
- 2020
Let $\Sigma$ be a compact oriented surface and $N$ a compact Kahler manifold with nonnegative holomorphic bisectional curvature. For harmonic map flow starting from a map $\Sigma \to N$ with low…
References
SHOWING 1-10 OF 20 REFERENCES
Partial differential equations
- Mathematics
- 1953
Many physical problems involve quantities that depend on more than one variable. The temperature within a “large”1 solid body of conducting material varies with both time and location within the…
Complex Analytic Coordinates in Almost Complex Manifolds
- Mathematics
- 1957
A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic…
Topology of three dimensional manifolds and the embedding problems in minimal surface theory
- Mathematics
- 1980
The Complex-Analyticity of Harmonic Maps and the Strong Rigidity of Compact Kahler Manifolds
- Mathematics
- 1980
Closedness of the Douady Spaces of Compact Kähler Spaces
- Mathematics
- 1978
Let X be a complex space and Dx the Douady space of compact analytic subspaces of X. For every point d^Dx-> we denote by Zd the corresponding analytic subspace of X. Define the subspace, Dx, of…
Three-dimensional compact Kähler manifolds with positive holomorphic bisectional curvature
- Mathematics
- 1972
On univalent harmonic maps between surfaces
- Mathematics
- 1978
Hence the energy defines a functional on the space of Lipshitz maps between M and M'. Critical points of this functional are called harmonic maps. These maps were studied by Bochner, Morrey, Rauch,…