12 citations · 59 across the 21 of their papers we have counts for
23 papers
Boundary regularity of harmonic map heat flows from RCD spaces into spaces
Zi-Ying Liu, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we study the boundary regularity of harmonic map heat flows from a bounded domain in a metric measure space with generalized Ricci curvature bounded from below into…
Lipschitz regularity of harmonic map heat flows from spaces into spaces
Bang-Xian Han, Hui-Chun Zhang, Xi-Ping Zhu
We prove positive-time regularity for harmonic map heat flows from finite-dimensional spaces into complete spaces, without assuming that eithe…
Lipschitz regularity of harmonic map heat flows into spaces
Hui-Chun Zhang, Xi-Ping Zhu
In 1964, Eells and Sampson proved the celebrated long-time existence and convergence for the harmonic map heat flow into non-positively curved Riemannian manifolds. In 1992, Gromov…
Optimal boundary regularity of harmonic maps from -spaces to -spaces
Hui-Chun Zhang, Xi-Ping Zhu
In 1983, Schoen-Uhlenbeck \cite{SU83} established boundary regularity for energy-minimizing maps between smooth manifolds with the Dirichlet boundary condition under the assumption…
Comments on the regularity of harmonic maps between singular spaces
Luca Gennaioli, Nicola Gigli, Hui-Chun Zhang +1
In this work we are going to establish Hölder continuity of harmonic maps from an open set in an space valued into a space, with the constraint…
Boundary Regularity of Harmonic maps from -space to -space
Hui-Chun Zhang, Xi-Ping Zhu
We establish the boundary regularity of harmonic maps from metric measure spaces into metric spaces.
Weyl's lemma on metric measure spaces
Yu Peng, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we extend the classical Weyl's lemma to metric measure spaces. As its applications, we show the local regularity of solutions for Poisson equations and a…
One-phase Free Boundary Problems on RCD Metric Measure Spaces
Chung-Kwong Chan, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we consider a vector-valued one-phase Bernoulli-type free boundary problem on a metric measure space with Riemannian curvature-dimension condition $RCD(K,N…
Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds
Bing Wang, Hui-Chun Zhang
In this paper, we generalize Liouville type theorems for some semilinear partial differential inequalities to sub-Riemannian manifolds satisfying a nonnegative generalized curvatur…
Partial regularity of harmonic maps from Alexandrov spaces
Huabin Ge, Wenshuai Jiang, Hui-Chun Zhang
In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conj…
Quantitative gradient estimates for harmonic maps into singular spaces
Hui-Chun Zhang, Xiao Zhong, Xi-Ping Zhu
In this paper, we will show the Yau's gradient estimate for harmonic maps into a metric space with curvature bounded above by a constant , , in the sense of Al…
Sharp gradient estimate for heat kernels on metric measure spaces
Jia-Cheng Huang, Hui-Chun Zhang
In this paper, we will establish an elliptic local Li-Yau gradient estimate for weak solutions of the heat equation on metric measure spaces with generalized Ricci curvature bounde…
Weyl's law on metric measure spaces
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.
Local Li-Yau's estimates on metric measure spaces
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove…
Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces
Renjin Jiang, Huichun Zhang
In this paper, we extend the Hamilton's gradient estimates \cite{har93} and a monotonicity formula of entropy \cite{ni04} for heat flows from smooth Riemannian manifolds to (non-sm…
Sharp Spectral Gaps on Metric Measure Spaces
Yin Jiang, Hui-Chun Zhang
In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to gener…
Heat Kernel Bounds on Metric Measure Spaces and Some Applications
Renjin Jiang, Huaiqian Li, Huichun Zhang
Let be a space with and . For , we derive the upper and lower bounds of the heat kernel on …
A note on Liouville type theorem of elliptic inequality on Riemannian manifolds
Hui-Chun Zhang
Let and let be a complete Riemannian manifold. In a recent work [9], Grigoryan and Sun proved that a pointwise upper bound of volume growth is sufficient for u…
Lipschitz continuity of harmonic maps between Alexandrov spaces
Hui-Chun Zhang, Xi-Ping Zhu
In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov…
Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces
Zhongmin Qian, Hui-Chun Zhang, Xi-Ping Zhu
In the previous work [35], the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochn…
Yau's gradient estimates on Alexandrov spaces
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau's gradient estimate for harmonic functions is also obtained on Alexa…
On a new definition of Ricci curvature on Alexandrov spaces
Hui-Chun Zhang, Xi-Ping Zhu
Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we extend our research to summarize the ge…
Ricci Curvature on Alexandrov spaces and Rigidity Theorems
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we introduce a new notion for lower bounds of Ricci curvature on Alexandrov spaces, and extend Cheeger-Gromoll splitting theorem and Cheng's maximal diameter theorem…