scholarly journals Calabi flow and projective embeddings

2010 ◽  
Vol 84 (3) ◽  
pp. 489-523 ◽  
Author(s):  
Joel Fine ◽  
Kefeng Liu ◽  
Xiaonan Ma
Keyword(s):  
Calabi Flow

scholarly journals Local Solution and Extension to the Calabi Flow

2011 ◽  
Vol 23 (1) ◽  
pp. 270-282 ◽  
Author(s):  
Weiyong He
Keyword(s):  
Local Solution ◽  
Calabi Flow

scholarly journals On the convergence of the Calabi flow

2014 ◽  
Vol 143 (3) ◽  
pp. 1273-1281 ◽  
Author(s):  
Weiyong He
Keyword(s):  
Calabi Flow

On combinatorial Calabi flow with hyperbolic circle patterns

2018 ◽  
Vol 333 ◽  
pp. 523-538 ◽  
Author(s):  
Huabin Ge ◽  
Bobo Hua
Keyword(s):  
Calabi Flow ◽  
Circle Patterns

scholarly journals Correction to: Regularity Scales and Convergence of the Calabi Flow

2018 ◽  
Vol 29 (3) ◽  
pp. 3010-3010
Author(s):  
Haozhao Li ◽  
Bing Wang ◽  
Kai Zheng
Keyword(s):  
Calabi Flow

Discrete Calabi Flow: A Unified Conformal Parameterization Method

2019 ◽  
Vol 38 (7) ◽  
pp. 707-720 ◽  
Author(s):  
KH Su ◽  
CC Li ◽  
YM Zhou ◽  
X Xu ◽  
XF Gu
Keyword(s):  
Parameterization Method ◽  
Calabi Flow

scholarly journals The Calabi Flow with Rough Initial Data

2019 ◽  
Author(s):  
Weiyong He ◽  
Yu Zeng
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Riemannian Manifolds ◽  
Kähler Metric ◽  
Calabi Flow ◽  
Existence Time ◽  
Rough Initial Data ◽  
Short Time ◽  
Kahler Metric ◽  
Time Existence

Abstract In this paper, we prove that there exists a dimensional constant $\delta> 0$ such that given any background Kähler metric $\omega $, the Calabi flow with initial data $u_0$ satisfying \begin{equation*} \partial \bar \partial u_0 \in L^\infty (M)\ \textrm{and}\ (1- \delta )\omega < \omega_{u_0} < (1+\delta )\omega, \end{equation*}admits a unique short-time solution, and it becomes smooth immediately, where $\omega _{u_0}: = \omega +\sqrt{-1}\partial \bar \partial u_0$. The existence time depends on initial data $u_0$ and the metric $\omega $. As a corollary, we get that the Calabi flow has short-time existence for any initial data satisfying \begin{equation*} \partial \bar \partial u_0 \in C^0(M)\ \textrm{and}\ \omega_{u_0}> 0, \end{equation*}which should be interpreted as a “continuous Kähler metric”. A main technical ingredient is a new Schauder-type estimates for biharmonic heat equation on Riemannian manifolds with time-weighted Hölder norms.

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