Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds
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| Format: | Preprint |
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2025
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| _version_ | 1866911175358283776 |
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| author | Hsiao, Chin-Yu Huang, Rung-Tzung Shao, Guokuan |
| author_facet | Hsiao, Chin-Yu Huang, Rung-Tzung Shao, Guokuan |
| contents | Let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small time asymptotics of the heat kernel of Kohn Laplacian. Suppose that condition $Y(q)$ fails, we establish the small time asymptotics of the kernel of the difference of the heat operator and Szegő projector. As an application we define the analytic torsion on a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form. Let $L^k$ be the $k$-th power of a CR complex line bundle $L$ over $X$. We also establish asymptotics of the analytic torsion with values in $L^k$ under certain natural assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds Hsiao, Chin-Yu Huang, Rung-Tzung Shao, Guokuan Differential Geometry Complex Variables Let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small time asymptotics of the heat kernel of Kohn Laplacian. Suppose that condition $Y(q)$ fails, we establish the small time asymptotics of the kernel of the difference of the heat operator and Szegő projector. As an application we define the analytic torsion on a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form. Let $L^k$ be the $k$-th power of a CR complex line bundle $L$ over $X$. We also establish asymptotics of the analytic torsion with values in $L^k$ under certain natural assumptions. |
| title | Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2509.19167 |