서브메뉴
검색
Capillary Hypersurfaces and Variational Methods in Positively Curved Manifolds with Boundary
Capillary Hypersurfaces and Variational Methods in Positively Curved Manifolds with Boundary
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104854
- ISBN
- 9798288814600
- DDC
- 516.22
- 저자명
- Wu, Yujie.
- 서명/저자
- Capillary Hypersurfaces and Variational Methods in Positively Curved Manifolds with Boundary
- 발행사항
- [Sl] : Stanford University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 112 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
- 주기사항
- Advisor: Chodosh, Otis.
- 학위논문주기
- Thesis (Ph.D.)--Stanford University, 2025.
- 초록/해제
- 요약We study free boundary and capillary minimal hypersurfaces from the variational point of view-- they are critical point to the area functional with certain prescribed boundary condition. In particular, we study the interaction of these objects with scalar curvature and boundary convexity. We first apply the method of generalized soap bubbles (μ-bubbles) to study manifolds with positive scalar curvature; we prove a rigidity result for free boundary minimal hypersurfaces in a 4-manifolds with certain positivity assumptions on curvature. Then we define generalized capillary surfaces (θ-bubbles) and use θbubbles to obtain geometric estimates on manifolds with non-negative scalar curvature and uniformly mean convex boundary, including a 1-Urysohn width bound and bandwidth estimate for such 3-manifolds. Lastly, the method of θ-bubble allows us to swap the assumption of positive scalar curvature when using the $\\mu$-bubble method with the assumption of positive mean curvature of the boundary, obtaining analogous rigidity results for free boundary minimal hypersurfaces.
- 일반주제명
- Euclidean space
- 일반주제명
- Inequality
- 일반주제명
- Geometry
- 일반주제명
- Topological manifolds
- 일반주제명
- Mathematics
- 기타저자
- Stanford University.
- 기본자료저록
- Dissertations Abstracts International. 87-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008260126s2025 us c eng d■001000017359242
■00520260202104854
■006m o d
■007cr#unu||||||||
■020 ▼a9798288814600
■035 ▼a(MiAaPQ)AAI32200997
■035 ▼a(MiAaPQ)Stanfordtg437cn1892
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a516.22
■1001 ▼aWu, Yujie.
■24510▼aCapillary Hypersurfaces and Variational Methods in Positively Curved Manifolds with Boundary
■260 ▼a[Sl]▼bStanford University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a112 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-02, Section: B.
■500 ▼aAdvisor: Chodosh, Otis.
■5021 ▼aThesis (Ph.D.)--Stanford University, 2025.
■520 ▼aWe study free boundary and capillary minimal hypersurfaces from the variational point of view-- they are critical point to the area functional with certain prescribed boundary condition. In particular, we study the interaction of these objects with scalar curvature and boundary convexity. We first apply the method of generalized soap bubbles (μ-bubbles) to study manifolds with positive scalar curvature; we prove a rigidity result for free boundary minimal hypersurfaces in a 4-manifolds with certain positivity assumptions on curvature. Then we define generalized capillary surfaces (θ-bubbles) and use θbubbles to obtain geometric estimates on manifolds with non-negative scalar curvature and uniformly mean convex boundary, including a 1-Urysohn width bound and bandwidth estimate for such 3-manifolds. Lastly, the method of θ-bubble allows us to swap the assumption of positive scalar curvature when using the $\\mu$-bubble method with the assumption of positive mean curvature of the boundary, obtaining analogous rigidity results for free boundary minimal hypersurfaces.
■590 ▼aSchool code: 0212.
■650 4▼aEuclidean space
■650 4▼aInequality
■650 4▼aGeometry
■650 4▼aTopological manifolds
■650 4▼aMathematics
■690 ▼a0405
■71020▼aStanford University.
■7730 ▼tDissertations Abstracts International▼g87-02B.
■790 ▼a0212
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359242▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
