48 citations · 178 across the 30 of their papers we have counts for
32 papers
Liouville theorem for a class of Hessian equations
Jianchun Chu, Sławomir Dinew
In this paper, we study a general class of Hessian elliptic equations, including the Monge-Ampère equation, the -Hessian equation and -Monge-Ampère equations. We propose new…
A non-spin method to the positive weighted mass theorem for weighted manifolds
Jianchun Chu, Jintian Zhu
In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of -scalar…
Singular positive mass theorem with arbitrary ends
Jianchun Chu, Man-Chun Lee, Jintian Zhu
Motivated by the recent progress on positive mass theorem for asymptotically flat manifolds with arbitrary ends and the Gromov's definition of scalar curvature lower bound for cont…
Rigidity on non-negative intermediate curvature
Jianchun Chu, Kwok-Kun Kwong, Man-Chun Lee
In a recent work of Brendle-Hirsch-Johne, a notion of intermediate curvature was introduced to extend the classical non-existence theorem of positive scalar curvature on torus to p…
Ricci-Deturck flow from rough metrics and applications
Jianchun Chu, Man-Chun Lee
Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and h…
Lelong Numbers of -Subharmonic Functions Along Submanifolds
Jianchun Chu, Nicholas McCleerey
We study the possible singularities of an -subharmonic function along a complex submanifold of a compact Kähler manifold, finding a maximal rate of growth for which…
Monotonicity of the -Green functions
Pak-Yeung Chan, Jianchun Chu, Man-Chun Lee +1
On a complete -nonparabolic -dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper $…
Kähler tori with almost non-negative scalar curvature
Jianchun Chu, Man-Chun Lee
Motivated by the torus stability problem, in this work we study Kähler metrics with almost non-negative scalar curvature on complex torus. We prove that after passing to a subseque…
Fully non-linear elliptic equations on compact almost Hermitian manifolds
Jianchun Chu, Liding Huang, Jiaogen Zhang
In this paper, we establish a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we solve the…
Hypercritical deformed Hermitian-Yang-Mills equation
Jianchun Chu, Man-Chun Lee
In this work, we study the deformed Hermitian-Yang-Mills equation on compact Kähler manifold. We introduce the notions of coerciveness and properness of the -functiona…
A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation
Jianchun Chu, Man-Chun Lee, Ryosuke Takahashi
The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact Kähler manifolds that corresponds to the special Lagrangian equation in the context of the Strom…
On the Hölder estimate of Kähler-Ricci flow
Jianchun Chu, Man-Chun Lee
In this work, we study the H\"older regularity of the Kähler- Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By adapting the method in the work of…
Conformal tori with almost non-negative scalar curvature
Jianchun Chu, Man-Chun Lee
In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the sequence is uniformly conformal to another sequence of metrics…
Fully non-linear degenerate elliptic equations in complex geometry
Jianchun Chu, Nicholas McCleerey
We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of…
Kähler manifolds and mixed curvature
Jianchun Chu, Man-Chun Lee, Luen-Fai Tam
In this work we consider compact Kähler manifolds with non-positive mixed curvature which is a "convex combination" of Ricci curvature and holomorphic sectional curvature. We show…
Curvature estimates for a class of Hessian type equations
Jianchun Chu, Heming Jiao
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
A simple proof of curvature estimate for convex solution of -Hessian equation
Jianchun Chu
Guan-Ren-Wang established the curvature estimate of convex hypersurface satisfying the Weingarten curvature equation . In this note, we give a simple proof…
The space of almost calibrated forms on a compact Kähler manifold
Jianchun Chu, Tristan C. Collins, Man-Chun Lee
The space of "almost calibrated" forms on a compact Kähler manifold plays an important role in the study of the deformed Hermitian-Yang-Mills equation of mirr…
regularity of geodesics of singular Kähler metrics
Jianchun Chu, Nicholas McCleerey
We show the optimal regularity of geodesics in nef and big cohomology class on Kähler manifolds away from the non-Kähler locus, assuming sufficiently regular initial data…
regularity of degenerate complex Monge-Ampère equations and some applications
Jianchun Chu
In this paper, we prove a estimate for solutions of complex Monge-Ampère equations on compact almost Hermitian manifolds. Using this estimate, we show existence…
regularity of geodesics in the space of volume forms
Jianchun Chu
We prove a estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the regularity of geodesics in the…
The Fu-Yau equation on compact astheno-Kähler manifolds
Jianchun Chu, Liding Huang, Xiaohua Zhu
In this paper, we study the Fu-Yau equation on compact Hermitian manifolds and prove the existence of solutions of equation on astheno-Kähler manifolds. We also prove the uniquenes…
The Fu-Yau equation in higher dimensions
Jianchun Chu, Liding Huang, Xiaohua Zhu
In this paper, we prove the existence of solutions to the Fu-Yau equation on compact Kähler manifolds. As an application, we give a class of non-trivial solutions of the modified S…
The -nd Hessian type equation on almost Hermitian manifolds
Jianchun Chu, Liding Huang, Xiaohua Zhu
In this paper, we derive the second order estimate to the -nd Hessian type equation on a compact almost Hermitian manifold.