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Heat Kernel Estimates on Glued Spaces
Heat Kernel Estimates on Glued Spaces
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151321
- ISBN
- 9798382841090
- DDC
- 510
- 서명/저자
- Heat Kernel Estimates on Glued Spaces
- 발행사항
- [Sl] : Cornell University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 215 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Saloff-Coste, Laurent.
- 학위논문주기
- Thesis (Ph.D.)--Cornell University, 2024.
- 초록/해제
- 요약In this thesis, we prove heat kernel estimates in two main contexts: (1) manifolds with ends with mixed Dirichlet and Neumann boundary condition and (2) infinite (countable) graphs satisfying certain properties, which we call book-like graphs. In both of these settings, we start with "sufficiently nice" pieces (pieces satisfying two-sided Gaussian heat kernel estimates) that are "glued" together in some sufficiently nice way. The results in setting (1) extend previous results of Grigor'yan and Saloff-Coste in the case of manifolds with ends with Neumann (or no) boundary condition. In setting (2), we are in the discrete case, where there is not direct prior work. This thesis extends some of the continuous setting results of Grigor'yan and Saloff-Coste mentioned above to the discrete setting, and the results here are also related to results of Grigor'yan and Ishiwata regarding gluing two copies of ℝn via a surface of revolution. In both settings, the results of this thesis rely heavily on the h-transform technique and understanding particular harmonic functions and hitting probabilities. In the setting of (1), we show the existence of a global harmonic function satisfying particular properties. In the setting of (2), we give estimates on certain hitting probabilities that naturally arise from considering subgraphs of larger graphs. All work in this thesis is joint with Laurent Saloff-Coste.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 기타저자
- Cornell University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211151321
■006m o d
■007cr#unu||||||||
■020 ▼a9798382841090
■035 ▼a(MiAaPQ)AAI31239327
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aDautenhahn, Emily.▼0(orcid)0000-0003-1953-6369
■24510▼aHeat Kernel Estimates on Glued Spaces
■260 ▼a[Sl]▼bCornell University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a215 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Saloff-Coste, Laurent.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aIn this thesis, we prove heat kernel estimates in two main contexts: (1) manifolds with ends with mixed Dirichlet and Neumann boundary condition and (2) infinite (countable) graphs satisfying certain properties, which we call book-like graphs. In both of these settings, we start with "sufficiently nice" pieces (pieces satisfying two-sided Gaussian heat kernel estimates) that are "glued" together in some sufficiently nice way. The results in setting (1) extend previous results of Grigor'yan and Saloff-Coste in the case of manifolds with ends with Neumann (or no) boundary condition. In setting (2), we are in the discrete case, where there is not direct prior work. This thesis extends some of the continuous setting results of Grigor'yan and Saloff-Coste mentioned above to the discrete setting, and the results here are also related to results of Grigor'yan and Ishiwata regarding gluing two copies of ℝn via a surface of revolution. In both settings, the results of this thesis rely heavily on the h-transform technique and understanding particular harmonic functions and hitting probabilities. In the setting of (1), we show the existence of a global harmonic function satisfying particular properties. In the setting of (2), we give estimates on certain hitting probabilities that naturally arise from considering subgraphs of larger graphs. All work in this thesis is joint with Laurent Saloff-Coste.
■590 ▼aSchool code: 0058.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aHarnack inequality
■653 ▼aHeat kernel estimates
■653 ▼aHarmonic functions
■690 ▼a0405
■690 ▼a0364
■71020▼aCornell University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161183▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
