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Stability for Area in Codimension One
Stability for Area in Codimension One
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103158
- ISBN
- 9798280747043
- DDC
- 510
- 서명/저자
- Stability for Area in Codimension One
- 발행사항
- [Sl] : Princeton University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 167 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Coda Marques, Fernando.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2025.
- 초록/해제
- 요약We present three results investigating aspects of the stability of minimal hypersurfaces.First, in joint work with Otis Chodosh, Chao Li, and Paul Minter, we prove that every complete oriented stable minimal hypersurface in ℝ5 is a hyperplane, which settles the stable Bernstein problem in dimension 5. Some consequences of this classification are curvature estimates for stable minimal hypersurfaces in 5-dimensional Riemannian manifolds.Second, in joint work with Otis Chodosh and Chao Li, we prove a rigidity result for complete two-sided stable minimal hypersurfaces in 4-dimensional manifolds with bounded and nonnegative sectional curvature and uniformly positive scalar curvature. We use this rigidity result to prove new topological obstructions for complete noncompact 4-dimensional manifolds satisfying these curvature assumptions.Finally, we present a new localization technique to prove the existence of minimal hypersurfaces in some complete noncompact manifolds. The minimal hypersurfaces produced by these methods are not necessarily stable, but they are quantitatively almost stable (index at most one). This result can be viewed as the sharp generalization to complete noncompact manifolds of the successful min-max theory of minimal hypersurfaces in closed manifolds.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 키워드
- Codimension one
- 키워드
- Manifolds
- 키워드
- Euclidean space
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798280747043
■035 ▼a(MiAaPQ)AAI31998344
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aStryker, Douglas.
■24510▼aStability for Area in Codimension One
■260 ▼a[Sl]▼bPrinceton University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a167 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Coda Marques, Fernando.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2025.
■520 ▼aWe present three results investigating aspects of the stability of minimal hypersurfaces.First, in joint work with Otis Chodosh, Chao Li, and Paul Minter, we prove that every complete oriented stable minimal hypersurface in ℝ5 is a hyperplane, which settles the stable Bernstein problem in dimension 5. Some consequences of this classification are curvature estimates for stable minimal hypersurfaces in 5-dimensional Riemannian manifolds.Second, in joint work with Otis Chodosh and Chao Li, we prove a rigidity result for complete two-sided stable minimal hypersurfaces in 4-dimensional manifolds with bounded and nonnegative sectional curvature and uniformly positive scalar curvature. We use this rigidity result to prove new topological obstructions for complete noncompact 4-dimensional manifolds satisfying these curvature assumptions.Finally, we present a new localization technique to prove the existence of minimal hypersurfaces in some complete noncompact manifolds. The minimal hypersurfaces produced by these methods are not necessarily stable, but they are quantitatively almost stable (index at most one). This result can be viewed as the sharp generalization to complete noncompact manifolds of the successful min-max theory of minimal hypersurfaces in closed manifolds.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aMinimal hypersurfaces
■653 ▼aCodimension one
■653 ▼aManifolds
■653 ▼aCurvature assumptions
■653 ▼aEuclidean space
■690 ▼a0405
■690 ▼a0642
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357267▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
