Evolution of the Steklov eigenvalue under geodesic curvature flow
측지곡률 변화에 따른 스테클로브 고윳값의 변화
- 주제(키워드) Steklov eigenvalue , geodesic curvature flow
- 발행기관 서강대학교 일반대학원
- 지도교수 Ho, Pak Tung
- 발행년도 2018
- 학위수여년월 2018. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000063397
- UCI I804:11029-000000063397
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
In section 3, we are going to recall some basic definitions and theorems in Riemannian geometry. In particular, we will define the eigenvalues and the Steklov eigenvalues. Then we will talk about the conformal metrics and some of their properties. And finally, we talk about geometric flows, especially, the geodesic curvature flow. In section 4, we prove the following results on two-dimensional manifolds with boundary: if the initial metric has positive geodesic curvature and vanishing Gaussian curvature, then the first nonzero Steklov eigenvalue is nondecreasing along the unnormalized geodesic curvature flow. And we will derive some estimates for the first nonzero Steklov eigenvalue by using the normalized geodesic curvature flow.
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