# Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with $S^1$ action

@article{Cheng2015HeatKA, title={Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with \$S^1\$ action}, author={Jih-Hsin Cheng and Chin-Yu Hsiao and I Hsun Tsai}, journal={arXiv: Differential Geometry}, year={2015} }

Among those transversally elliptic operators initiated by Atiyah and Singer, Kohn's $\Box_b$ operator on CR manifolds with $S^1$ action is a natural one of geometric significance for complex analysts. Our first main result establishes an asymptotic expansion for the heat kernel of such an operator with values in its Fourier components, which involves an unprecedented contribution in terms of a distance function from lower dimensional strata of the $S^1$-action. Our second main result computes a…

## 5 Citations

A Local Index Theorem of Transversal Type on Manifolds with Locally Free $\mathbb{S}^1$-action

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We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free $\mathbb{S}^1$-action. One difficulty of using heat kernel method lies in the understanding of…

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Abstract 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 S 1 -action is transversal on…

Szegö kernel asymptotic expansion on strongly pseudoconvex CR manifolds with S1 action

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Let [Formula: see text] be a compact connected strongly pseudoconvex Cauchy–Riemann (CR) manifold of real dimension [Formula: see text] with a transversal CR [Formula: see text] action on [Formula:…

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

- Mathematics
- 2016

We prove the stability of the equivariant embedding of compact strictly pseudoconvex CR manifolds with transversal CR circle action under circle invariant deformations of the CR structures.

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