Xiangsheng Wang

works on

dirac operator 1 positive mass theorem 1 scalar curvature 1 spectral condition 1 spin geometry 1

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math.DG2026

The positive mass theorem under a spectral scalar curvature bound on spin manifolds

Xiangsheng Wang

The paper proves Brendle and Wang’s refined positive mass theorem on spin manifolds using Dirac operator methods and explains the origin of the special coefficient in their spectra…

math.DG2026

Generalized moment maps, reduction and complex quotients

Yi Hu, Xiangsheng Wang

In this note, we introduce the concept of momentumly closed forms. A non-degenerate momentumly closed two-form and its generalized moment map are the generalization of two well-kno…

math.DG2025

$K$ -cowaist on complete foliated manifolds

Guangxiang Su, Xiangsheng Wang

Let $(M, F)$ be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric $g^{T M}$ . We generalize Gromov's $K$ -cowaist using the coverin…

math.DG2024

The complex hyperbolic form as a Weil-Petersson form

Xiangsheng Wang

For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singu…

math.DG2024

Llarull's theorem on odd dimensional manifolds: the noncompact case

Yihan Li, Guangxiang Su, Xiangsheng Wang +1

Let $(M, g^{T M})$ be an odd dimensional ( $dim M \geq 3$ ) connected oriented noncompact complete spin Riemannian manifold. Let $k^{T M}$ be the associated scalar curvature. Let $f:M\t…

The positive mass theorem under a spectral scalar curvature bound on spin manifolds

Generalized moment maps, reduction and complex quotients

K-cowaist on complete foliated manifolds

The complex hyperbolic form as a Weil-Petersson form

Llarull's theorem on odd dimensional manifolds: the noncompact case

$K$ -cowaist on complete foliated manifolds