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arXiv · 1110.3206

Bounding the first Dirichlet eigenvalue of a tube around a complex submanifold of $CP^n$ by the degrees of the polynomials defining it

M. Carmen Domingo-Juan·Vicente Miquel
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Abstract

We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold $P$ of $CP^n$ which depends only on the radius of the tube, the degrees of the polynomials defining $P$ and the first eigenvalue of some model centers of the tube. The bounds are sharp on these models. Moreover, when the models used are $CP^q$ or the complex hyperquadric, these bounds also give gap phenomena and comparison results.

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M. Carmen Domingo-Juan, Vicente Miquel. 2011-10-14. Bounding the first Dirichlet eigenvalue of a tube around a complex submanifold of $CP^n$ by the degrees of the polynomials defining it. https://arxiv.org/abs/1110.3206

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