# 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… Expand

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