Xiaoshan Li

activity

20122026

most cited

S^{1}

-equivariant Index theorems and Morse inequalities on complex manifolds with boundary

7 citations · 34 across the 18 of their papers we have counts for

collaborators

19 papers

math.CV2026

CSC Bergman metrics are Einstein on pseudoconvex domains

Xiaoshan Li, Taishun Liu

Let $Ω \subset C^{n}$ ( $n \geq 3$ ) be a pseudoconvex domain with a smooth strongly pseudoconvex boundary point. We prove that if the Bergman metric of $Ω$ has constant scalar cur…

math.CV2026

A note on csc Bergman metric

Xiaojun Huang, Xiaoshan Li

In this note, we show that if the Bergman metric of a pseudoconvex domain in $C^{n}$ ( $n \geq 3$ ) has constant scalar curvature, then every strongly pseudoconvex boundary point…

math.CV2026

Localization of Bergman Kernels and the Cheng-Yau Conjecture on Real Analytic Pseudoconvex Domains

Chin-Yu Hsiao, Xiaojun Huang, Xiaoshan Li

In this paper, we establish the localization of Bergman kernels for unbounded pseudoconvex domains near boundary points of finite D'Angelo type. This result was proved by Engliš mo…

math.CV2023

$G$ -invariant Bergman kernel and geometric quantization on complex manifolds with boundary

Chin-Yu Hsiao, Rung-Tzung Huang, Xiaoshan Li +1

Let $M$ be a complex manifold with boundary $X$ , which admits a holomorphic Lie group $G$ -action preserving $X$ . We establish a full asymptotic expansion for the $G$ -invariant Berg…

math.CV2022★ 2 cited

On Bergman kernel functions and weak Morse inequalities

Xiaoshan Li, Guokuan Shao, Huan Wang

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$ -convex manifolds, pseudoconvex domains, weakly $1$ -complete manifolds and coveri…

math.CV2022

Semi-classical asymptotics of partial Bergman kernels on $R$ -symmetric complex manifolds with boundary

Chin-Yu Hsiao, Xiaoshan Li, George Marinescu

Let $M$ be a relatively compact connected open subset with smooth connected boundary of a complex manifold $M^{'}$ . Let $(L, h^{L}) \to M^{'}$ be a positive line bundle over $M^{'}$ . Su…

math.CV2020★ 1 cited

Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary

Xiaojun Huang, Xiaoshan Li

Let $Ω$ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $Reg (Ω)$ is Kähler-Einstein…

math.CV2019

On a Holomorphic Family of Stein Manifolds with Strongly Pseudoconvex Boundaries

Xiaoshan Li, Guicong Su

We study the stable embedding problem for a CR family of 3-dimensional strongly pseudoconvex CR manifolds with each fiber bounding a stein manifold.

math.CV2018★ 1 cited

Torus equivariant Szegő kernel asymptotics on strongly pseudoconvex CR manifolds

Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li

Let $(X, T^{1, 0} X)$ be a compact strongly pseudoconvex CR manifold of dimension $2 n + 1$ . Assume that $X$ admits a Torus action $T^{d}$ . In this work, we study the behavior of torus eq…

math.CV2017★ 7 cited

$S^{1}$ -equivariant Index theorems and Morse inequalities on complex manifolds with boundary

Chin-Yu Hsiao, Rung-Tzung Huang, Xiaoshan Li +1

Let $M$ be a complex manifold of dimension $n$ with smooth connected boundary $X$ . Assume that $M$ admits a holomorphic $S^{1}$ -action preserving the boundary $X$ and the $…

math.CV2017★ 3 cited

Szegő kernels and equivariant embedding theorems for CR manifolds

Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li

We consider a compact connected CR manifold with a transversal CR locally free $R$ -action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fou…

math.CV2017

An explicit formula for Szego kernels on the Heisenberg group

Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li

In this paper, we give an explicit formula for the Szego kernel for $(0, q)$ forms on the Heisenberg group $H_{n + 1}$ .

math.CV2016★ 6 cited

Szegő kernel asymptotic expansion on CR manifolds with $S^{1}$ action

Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li

Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2 n + 1, n \geq 1$ with a transversal CR $S^{1}$ action on $X$ . We establish an asymptotic expansion for th…

math.CV2016★ 4 cited

On the stability of equivariant embedding of compact CR manifolds with circle action

Chin-Yu Hsiao, Xiaoshan Li, George Marinescu

We prove the stability of the equivariant embedding of compact strictly pseudoconvex CR manifolds with transversal CR circle action under circle invariant perturbations of the CR s…

math.CV2016

Equivariant Kodaira embedding of CR manifolds with circle action

Chin-Yu Hsiao, Xiaoshan Li, George Marinescu

We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kern…

math.CV2015★ 4 cited

Szegő kernel expansion and equivariant embedding of CR manifolds with circle action

Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li

Let $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^{1}$ -action. In this paper, we establish the asymptotic expansion of Szegő kernels of positive Fourier…

math.CV2015★ 6 cited

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with $S^{1}$ -action

Chin-Yu Hsiao, Xiaoshan Li

Let $X$ be a compact connected CR manifold of dimension $2 n - 1, n \geq 2$ with a transversal CR $S^{1}$ -action on $X$ . We study the Fourier components of the Kohn-Rossi cohomology with…

math.CV2014

Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces

Xiaojun Huang, Xiaoshan Li, Ming Xiao

We study the holomorphic embedding problem from a compact strongly pseudoconvex real algebraic hypersurface into a sphere of higher dimension. We construct a family of compact stro…

math.CV2012

$\partial$ -Equation on a Lunar Domain with Mixed Boundary Conditions

Xiaojun Huang, Xiaoshan Li

In this paper, making use of the method developed by Catlin and Catlin-Cho,we study the $L^{2}$ -estimate for the mixed boundary conditions on a lunar manifold with the mixed boundary…

CSC Bergman metrics are Einstein on pseudoconvex domains

A note on csc Bergman metric

Localization of Bergman Kernels and the Cheng-Yau Conjecture on Real Analytic Pseudoconvex Domains

G-invariant Bergman kernel and geometric quantization on complex manifolds with boundary

On Bergman kernel functions and weak Morse inequalities

Semi-classical asymptotics of partial Bergman kernels on R-symmetric complex manifolds with boundary

Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary

On a Holomorphic Family of Stein Manifolds with Strongly Pseudoconvex Boundaries

Torus equivariant Szegő kernel asymptotics on strongly pseudoconvex CR manifolds

S1-equivariant Index theorems and Morse inequalities on complex manifolds with boundary

Szegő kernels and equivariant embedding theorems for CR manifolds

An explicit formula for Szego kernels on the Heisenberg group

Szegő kernel asymptotic expansion on CR manifolds with S1 action

On the stability of equivariant embedding of compact CR manifolds with circle action

Equivariant Kodaira embedding of CR manifolds with circle action

Szegő kernel expansion and equivariant embedding of CR manifolds with circle action

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with S1-action

Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces

∂-Equation on a Lunar Domain with Mixed Boundary Conditions

$G$ -invariant Bergman kernel and geometric quantization on complex manifolds with boundary

Semi-classical asymptotics of partial Bergman kernels on $R$ -symmetric complex manifolds with boundary

$S^{1}$ -equivariant Index theorems and Morse inequalities on complex manifolds with boundary

Szegő kernel asymptotic expansion on CR manifolds with $S^{1}$ action

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with $S^{1}$ -action

$\partial$ -Equation on a Lunar Domain with Mixed Boundary Conditions