Guokuan Shao

activity

20152026

most cited

S^{1}

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

7 citations · 11 across the 14 of their papers we have counts for

collaborators

16 papers

math.CV2026

Unique continuation property for $\partial ˉ$ with $L^{2 n}$ potentials

Guokuan Shao, Ziming Shi, Jujie Wu

We establish the sharp unique continuation property for the Cauchy--Riemann operator $\partial ˉ$ in higher dimensions. Let $0\inΩ\subset \C^n$ be a domain. Suppose $u \in W_{\…

math.CV2026

Energy asymptotics of holomorphic functions with application to Calderón-Zygmund theory in $C$

Hongrong Chen, Guokuan Shao, Jujie Wu +1

The Calderón-Zygmund theory establishes the boundedness of singular integral operators on $L^{p}$ spaces for $1 < p < \infty$ , yet it encounters a failure at the endpoint $p = 1$ . Wh…

math.CV2026

Energy estimates for level sets of holomorphic functions and universal counterexamples to Calderón-Zygmund theory

Yifei Pan, Guokuan Shao, Jianfei Wang +1

We demonstrate that the failure of $L^{1}$ regularity in Calderón-Zygmund theory is a universal phenomenon: every non-constant holomorphic function in $\C^n$ generates a counterexamp…

math.DG2025

Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds

Chin-Yu Hsiao, Rung-Tzung Huang, Guokuan Shao

The existence of small-time asymptotics for the heat kernel of the Kohn Laplacian on a general CR manifold has remained an open problem. In this paper, we resolve the problem in th…

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

On equidistribution theorem for multi-sequences of holomorphic line bundles

Manli Liu, Weixiong Mai, Guokuan Shao

Given several sequences of Hermitian holomorphic line bundles ${(L_{k p}, h_{k p})}_{p = 1}^{\infty}$ , we establish the distribution of common zeros of random holomorphic sections of…

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.CV2021

On the Bergman kernel in weighted monogenic Bargmann-Fock spaces

Weixiong Mai, Guokuan Shao

In this paper, we study the Bergman kernel $B_{φ} (x, y)$ of generalized Bargmann-Fock spaces in the setting of Clifford algebra. The versions of $L^{2}$ -estimate method and weighted sub…

math.CV2020

Asymptotics of G-equivariant Szegő kernels

Rung-Tzung Huang, Guokuan Shao

Let $(X, T^{1, 0} X)$ be a compact connected orientable CR manifold of dimension $2 n + 1$ with non-degenerate Levi curvature. Assume that $X$ admits a connected compact Lie group $G$ a…

math.CV2020

On the coefficients of the equivariant Szegő kernel asymptotic expansions

Chin-Yu Hsiao, Rung-Tzung Huang, Guokuan Shao

Let $(X, T^{1, 0} X)$ be a compact connected orientable strongly pseudoconvex CR manifold of dimension $2 n + 1$ , $n \geq 1$ . Assume that $X$ admits a connected compact Lie group $G$ acti…

math.CV2018★ 1 cited

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

Rung-Tzung Huang, Guokuan Shao

Let $X$ be a compact connected CR manifold of dimension $2 n + 1, n \geq 1$ . Let $X$ be a paracompact CR manifold with a transversal CR $S^{1}$ -action, such that there is a…

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

Equidistribution theorems on strongly pseudoconvex domains

Chin-Yu Hsiao, Guokuan Shao

This work consists of two parts. In the first part, we consider a compact connected strongly pseudoconvex CR manifold $X$ with a transversal CR $S^{1}$ action. We establish an equi…

math.CV2017

Convergence speed of weighted Bergman kernels towards extremal functions

Guokuan Shao

We construct inner products by the Bernstein-Markov inequality on spaces of holomorphic sections of high powers of a line bundle. The corresponding weighted Bergman kernel function…

math.CV2015

Equidistribution on Big Line Bundles with Singular Metrics for Moderate Measures

Guokuan Shao

We establish an equidistribution theorem for the common zeros of random sections of high powers of several singular Hermitian big line bundles associated to moderate measures.

math.CV2015★ 1 cited

Equidistribution of Zeros of Random Holomorphic Sections for Moderate Measures

Guokuan Shao

We establish an equidistribution theorem for the zeros of random holomorphic sections of high powers of a positive holomorphic line bundle. The equidistribution is associated with…

Unique continuation property for ∂ˉ with L2n potentials

Energy asymptotics of holomorphic functions with application to Calderón-Zygmund theory in C

Energy estimates for level sets of holomorphic functions and universal counterexamples to Calderón-Zygmund theory

Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds

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

On equidistribution theorem for multi-sequences of holomorphic line bundles

On Bergman kernel functions and weak Morse inequalities

On the Bergman kernel in weighted monogenic Bargmann-Fock spaces

Asymptotics of G-equivariant Szegő kernels

On the coefficients of the equivariant Szegő kernel asymptotic expansions

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

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

Equidistribution theorems on strongly pseudoconvex domains

Convergence speed of weighted Bergman kernels towards extremal functions

Equidistribution on Big Line Bundles with Singular Metrics for Moderate Measures

Equidistribution of Zeros of Random Holomorphic Sections for Moderate Measures

Unique continuation property for $\partial ˉ$ with $L^{2 n}$ potentials

Energy asymptotics of holomorphic functions with application to Calderón-Zygmund theory in $C$

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

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

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