Zobrazeno 1 - 10
of 156
pro vyhledávání: '"Chu, Jianchun"'
In this work, we investigate compact K\"ahler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature considered in the
Externí odkaz:
http://arxiv.org/abs/2408.14043
The classical Llarull theorem states that a smooth metric on $n$-sphere cannot have scalar curvature no less than $n(n-1)$ and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove
Externí odkaz:
http://arxiv.org/abs/2405.19724
We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a number of a
Externí odkaz:
http://arxiv.org/abs/2402.03098
In this work, optimal rigidity results for eigenvalues on K\"ahler manifolds with positive Ricci lower bound are established. More precisely, for those K\"ahler manifolds whose first eigenvalue agrees with the Ricci lower bound, we show that the comp
Externí odkaz:
http://arxiv.org/abs/2401.15830
We prove for $n\in\{3,4,5\}$ that the connected sum of a closed aspherical $n$-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a q
Externí odkaz:
http://arxiv.org/abs/2312.04698
Autor:
Chu, Jianchun, Dinew, Sławomir
In this paper, we study a general class of Hessian elliptic equations, including the Monge-Amp\`ere equation, the $k$-Hessian equation and $p$-Monge-Amp\`ere equations. We propose new additional condition on the solution and prove Liouville theorem u
Externí odkaz:
http://arxiv.org/abs/2306.13825
Autor:
Chu, Jianchun, Zhu, Jintian
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 $P$-scalar curvature, we are able to prove the positive weighted mass theorem fo
Externí odkaz:
http://arxiv.org/abs/2305.12909
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 continuous metrics, we start a program on the positive mass theorem for as
Externí odkaz:
http://arxiv.org/abs/2210.08261
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 product manifolds. In this work, we study the rigidity when the interme
Externí odkaz:
http://arxiv.org/abs/2208.12240
Autor:
Chu, Jianchun, Lee, Man-Chun
In this paper, we study the hypercritical deformed Hermitian-Yang-Mills equation on compact K\"ahler manifolds and resolve two conjectures of Collins-Yau.
Externí odkaz:
http://arxiv.org/abs/2206.00387