12 papers
Uniruledness and the sign of total scalar curvature
Zehao Sha, Jian Wang
For every integer , we construct a smooth projective manifold of complex dimension whose canonical bundle is not pseudoeffective, or equivalently, which is uniruled,…
Scalar curvature on Kähler blow-ups and systolic inequalities
Zehao Sha, Jian Wang
In this paper, we develop the weighted level set method for a Kähler manifold admitting an almost holomorphic map to a possibly singular base , which is not uniruled.…
Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities
Marcus Khuri, Jian Wang, Jinmin Wang
We prove the Riemannian positive mass theorem in all dimensions for asymptotically flat -metrics with subcritical singular sets. More precisely, we consider complete asym…
Brownian Loops and the Selberg Zeta Function
Roman Lemonde, Jian Wang
We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy cl…
Hölder damping for fractional wave equations
Jian Wang, Ruoyu P. T. Wang
For fractional wave equations with low Hölder regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The e…
Nonembeddable contractible open manifolds arising from Whitehead doubling
Shijie Gu, Jian Wang, Yanqing Zou
We study a family of genus-one contractible open manifolds constructed by iterated Whitehead doubling from a nontrivial knot and an even half-twist . For each such pair, we…
Mass Lower Bounds for Asymptotically Locally Flat Manifolds
Marcus Khuri, Jian Wang
We establish positive mass type theorems for asymptotically locally flat (ALF) manifolds, which have asymptotic ends modeled on circle bundles over a Euclidean base with fibers of…
Totally acyclic complexes and homological invariants over arbitrary rings
Jian Wang, Yunxia Li, Jiangsheng Hu +1
In this paper, we investigate equivalent characterizations of the condition that every acyclic complex of projective, injective, or flat modules is totally acyclic over a general r…
Convex waves grazing convex obstacles to high order
Jian Wang, Mark Williams
In a recent paper [WW23] we studied the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze a conve…
The positive fundamental group of
Jian Wang, Qinglong Zhou
In this paper, we examine the homotopy classes of positive loops in . We demonstrate that two positive loops are homotopic if and only if they are homotopic through p…
On open manifolds admitting no complete metric with positive scalar curvature
Yuguang Shi, Jian Wang, Runzhang Wu +1
In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition f…
Transport of nonlinear oscillations along rays that graze a convex obstacle to any order
Jian Wang, Mark Williams
We provide a geometric optics description in spaces of low regularity, and , of the transport of oscillations in solutions to linear and some semilinear second-order hyp…