Chin-Yu Hsiao

activity

20082026

most citedAsymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles

72 citations · 201 across the 51 of their papers we have counts for

collaborators

57 papers

math.CV2026

Quantization Commutes with Reduction for Embeddable CR Reductions

Chin-Yu Hsiao, Rung-Tzung Huang, Xiaonan Ma +1

We prove a canonical quantization-commutes-with-reduction theorem for CR functions. Under the geometric hypotheses of Hsiao--Ma--Marinescu, if the zero moment level is nonempty and…

math.CV2026

Semi-classical heat kernel asymptotics on complex manifolds with boundary

Chin-Yu Hsiao, George Marinescu, Weixia Zhu

Let $M$ be a relatively compact open subset of a complex manifold $M^{'}$ with smooth boundary $X$ and let $L$ be a holomorphic line bundle over $M^{'}$ . Assuming that condition $Z (q)$ h…

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.CV2025

On the distribution kernels of Toeplitz operators on CR manifolds

Chin-Yu Hsiao, Ood Shabtai

We study the distribution kernel of a Toeplitz operator associated with a classical pseudodifferential operator on a compact, embeddable, strictly pseudoconvex CR manifold. The mai…

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.CV2025

Approximation of pseudohermitian structures via embeddings into spheres

Hendrik Herrmann, Chin-Yu Hsiao, Bernhard Lamel

Let $(X, T^{1, 0} X)$ be a compact strictly pseudoconvex CR manifold which is CR embeddable into the complex Euclidean space. We show that $T^{1, 0} X$ can be approximated in $\mathscr{…

math.CV2024

On the second coefficient in the semi-classical expansion of Toeplitz Operators

Chin-Chia Chang, Hendrik Herrmann, Chin-Yu Hsiao

Let $X$ be a compact strictly pseudoconvex embeddable CR manifold and let $A$ be the Toeplitz operator on $X$ associated with a Reeb vector field $\mathcal{T}\in\mathscr{C}^\infty(…

math.DG2024

Heat kernel and local index theorem for open complex manifolds with $C^{*}$ -action

Jih-Hsin Cheng, Chin-Yu Hsiao, I-Hsun Tsai

For a complex manifold $Σ$ with $C^{*}$ -action, we define the $m$ -th $C^{*}$ Fourier-Dolbeault cohomology group and consider the $m$ -index on $Σ$ . By appl…

math.CV2024

Quantization and reduction for torsion free CR manifolds

Andrea Galasso, Chin-Yu Hsiao

Consider a compact torsion free CR manifold $X$ and assume that $X$ admits a compact CR Lie group action $G$ . Let $L$ be a $G$ -equivariant rigid CR line bundle over $X$ . It seems n…

math.CV2024

Induced Fubini-Study metrics on strictly pseudoconvex CR manifolds and zeros of random CR functions

Hendrik Herrmann, Chin-Yu Hsiao, George Marinescu +1

Let $X$ be a compact strictly pseudoconvex embeddable Cauchy-Riemann manifold and let $T_{P}$ be the Toeplitz operator on $X$ associated with a first-order pseudodifferential operato…

math.CV2023

Semi-classical spectral asymptotics of Toeplitz operators on strictly pseudodonvex domains

Chin-Yu Hsiao, George Marinescu

On a relatively compact strictly pseudoconvex domain with smooth boundary in a complex manifold of dimension $n$ we consider a Toeplitz operator $T_{R}$ with symbol a Reeb-like vecto…

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.CV2023★ 1 cited

Semi-classical spectral asymptotics of Toeplitz operators on CR manifolds

Hendrik Herrmann, Chin-Yu Hsiao, George Marinescu +1

Let $X$ be a compact strictly pseudoconvex embeddable CR manifold and let $T_{P}$ be the Toeplitz operator on $X$ associated with some first order pseudodifferential operator $P$ . We…

math.DG2022

Embedding theorems for quantizable pseudo-Kähler manifolds

Andrea Galasso, Chin-Yu Hsiao

Given a compact quantizable pseudo-Kähler manifold $(M, ω)$ of constant signature, there exists a Hermitian line bundle $(L, h)$ over $M$ with curvature $- 2 π i ω$ . We shall show that…

math.CV2022

On the singularities of the Szegő kernels on CR orbifolds

Andrea Galasso, Chin-Yu Hsiao

In this paper we study the microlocal properties of the Szegő kernel of a given compact connected orientable CR orbifold whose Kohn Laplacian has closed range. This last assumption…

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.FA2021

Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds

Andrea Galasso, Chin-Yu Hsiao

Given a CR manifold with non-degenerate Levi form, we show that the operators of the functional calculus for Toeplitz operators are complex Fourier integral operators of Szegő type…

math.CV2021

Heat kernel asymptotics for Kohn Laplacians on CR manifolds

Chin-Yu Hsiao, Weixia Zhu

Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2 n + 1$ , $n \geq 1$ , and let $L^{k}$ be the $k$ -th tensor power of a CR complex line bundle $L$ over $…

math.CV2021

Toeplitz operators on CR manifolds and group actions

Andrea Galasso, Chin-Yu Hsiao

Let $(X, T^{1, 0} X)$ be a connected orientable compact CR manifold of dimension $2 n + 1$ , $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplit…

math.CV2021★ 1 cited

On the second coefficient of the asymptotic expansion of Boutet de Monvel--Sjöstrand

Chin-Yu Hsiao, Wei-Chuan Shen

In this paper, we calculate the second coefficient of the asymptotic expansion of Boutet de Monvel--Sjöstrand.

math.CV2020★ 4 cited

Szegő kernel asymptotics on some non-compact complete CR manifolds

Chin-Yu Hsiao, George Marinescu, Huan Wang

We establish Szegő kernel asymptotic expansions on non-compact strictly pseudoconvex complete CR manifolds with transversal CR $R$ -action under certain natural geometric c…

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.CV2020★ 1 cited

Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases

Chin-Yu Hsiao, Nikhil Savale

We construct a pointwise Boutet de Monvel-Sjöstrand parametrix for the Szegő kernel of a weakly pseudoconvex three dimensional CR manifold of finite type assuming the range of its…

math.CV2019

On the singularities of the Bergman projections for lower energy forms on complex manifolds with boundary

Chin-Yu Hsiao, George Marinescu

Let $M$ be a complex manifold of dimension $n$ with smooth boundary $X$ . Given $q \in {0, 1, \dots, n - 1}$ , let $□^{(q)}$ be the $\ddbar$-Neumann Laplacian for $(0, q)$ forms. We sh…

Quantization Commutes with Reduction for Embeddable CR Reductions

Semi-classical heat kernel asymptotics on complex manifolds with boundary

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

On the distribution kernels of Toeplitz operators on CR manifolds

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

Approximation of pseudohermitian structures via embeddings into spheres

On the second coefficient in the semi-classical expansion of Toeplitz Operators

Heat kernel and local index theorem for open complex manifolds with C∗-action

Quantization and reduction for torsion free CR manifolds

Induced Fubini-Study metrics on strictly pseudoconvex CR manifolds and zeros of random CR functions

Semi-classical spectral asymptotics of Toeplitz operators on strictly pseudodonvex domains

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

Semi-classical spectral asymptotics of Toeplitz operators on CR manifolds

Embedding theorems for quantizable pseudo-Kähler manifolds

On the singularities of the Szegő kernels on CR orbifolds

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

Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds

Heat kernel asymptotics for Kohn Laplacians on CR manifolds

Toeplitz operators on CR manifolds and group actions

On the second coefficient of the asymptotic expansion of Boutet de Monvel--Sjöstrand

Szegő kernel asymptotics on some non-compact complete CR manifolds

On the coefficients of the equivariant Szegő kernel asymptotic expansions

Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases

On the singularities of the Bergman projections for lower energy forms on complex manifolds with boundary

Heat kernel and local index theorem for open complex manifolds with $C^{*}$ -action

$G$ -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