A conformal lower bound of weighted Dirac eigenvalues on manifolds with boundary
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915854302576640 |
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| author | Zhang, Mingwei |
| author_facet | Zhang, Mingwei |
| contents | For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*}
\left\{ \begin{array}{ll} Dφ= λfφ& \text{in } M, \\ \mathbf{B}φ= 0 & \text{on } \partial M, \end{array} \right. \end{equation*} we first give a lower bound of the eigenvalue using the relative Yamabe constant
\begin{equation*}
λ^2 \geq \frac{n}{4(n-1)} Y(M,\partial M,[g]), \end{equation*} then prove that equality holds if and only if (up to a conformal transformation) $M$ is a hemisphere and $φ$ is a Killing spinor. More generalizations are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A conformal lower bound of weighted Dirac eigenvalues on manifolds with boundary Zhang, Mingwei Differential Geometry Mathematical Physics Analysis of PDEs For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*} \left\{ \begin{array}{ll} Dφ= λfφ& \text{in } M, \\ \mathbf{B}φ= 0 & \text{on } \partial M, \end{array} \right. \end{equation*} we first give a lower bound of the eigenvalue using the relative Yamabe constant \begin{equation*} λ^2 \geq \frac{n}{4(n-1)} Y(M,\partial M,[g]), \end{equation*} then prove that equality holds if and only if (up to a conformal transformation) $M$ is a hemisphere and $φ$ is a Killing spinor. More generalizations are studied. |
| title | A conformal lower bound of weighted Dirac eigenvalues on manifolds with boundary |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2603.10875 |