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Weyl's Law for Singular Algebraic Varieties
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Weyl's Law for Singular Algebraic Varieties. |
| 개인저자 | Kilgore, John. |
| 단체저자명 | University of Michigan. Mathematics. |
| 발행사항 | [S.l.]: University of Michigan., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 80 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-02B. Dissertation Abstract International |
| ISBN | 9781085672276 |
| 학위논문주기 | Thesis (Ph.D.)--University of Michigan, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Advisor: Ji, Lizhen. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | It is a classical result that the spectrum of the Laplacian on a compact Riemannian manifold forms a sequence going to positive infinity and satisfies an asymptotic growth rate known as Weyl's law determined by the volume and dimension of the manifold. Weyl's law motivated Kac's famous question, "Can one hear the shape of a drum?" which asks what geometric properties of a space can be determined by the spectrum of its Laplacian? I will show Weyl's law also holds for the non-singular locus of embedded, irreducible, singular projective algebraic varieties with the metric inherited from the Fubini-Study metric of complex projective space. This non-singular locus is a non-complete manifold with finite volume that comes from a very natural class of spaces which are extensively studied and used in many different disciplines of mathematics. Since the volume of a projective variety in the Fubini-Study metric is equal to its degree times the volume of the complex projective space of the same dimension, the result of this thesis shows the algebraic degree of a projective variety can be "heard" from its spectrum. The proof follows the heat kernel method of Minakshisundaram and Pleijel using heat kernel estimates of Li and Tian. Additionally, the eigenfunctions of the Laplacian on a singular variety will also be shown to satisfy a bound analogous to the known bound for the eigenfunctions of the Laplacian on a compact manifold. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
