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The Magnetic Ginzburg-Landau Equation: Stability, Regularity and Rigidity
The Magnetic Ginzburg-Landau Equation: Stability, Regularity and Rigidity
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103044
- ISBN
- 9798286425242
- DDC
- 510
- 저자명
- Halavati, Aria.
- 서명/저자
- The Magnetic Ginzburg-Landau Equation: Stability, Regularity and Rigidity
- 발행사항
- [Sl] : New York University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 249 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: De Philippis, Guido;Lin, Fang-Hua.
- 학위논문주기
- Thesis (Ph.D.)--New York University, 2025.
- 초록/해제
- 요약We study the magnetic Ginzburg-Landau energy in the critical coupling, also known as the abelian--Higgs model. It is known that entire solutions of the abelian-Higgs model blow down to (generalized) minimal submanifolds. We show that, in the so-called multiplicity one regime, critical points inherit an improvement of flatness and a rigidity property from their blow-down limit.This thesis consists of three parts. In the first two parts we develop the necessary toolbox for part three.First (in [44]), we develop a new class of weighted inequalities on any two-manifold (with boundary). Second (in [45]), using these inequalities and a selection principle (inspired by the quantitative isoperimetric inequality) we prove a sharp quantitative stability for the abelian-Higgs model in two dimensions.Third, (in a collaboration with Guido De Philippis and Alessandro Pigati in [28]) we leverage these tool to develop a large scale regularity theory for the zero set of solutions (in the spirit of Allard's). In fact, in the multiplicity one regime we show the uniqueness of blowdowns. Then we classify solutions in dimensions n 2.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Applied mathematics
- 기타저자
- New York 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 ▼a9798286425242
■035 ▼a(MiAaPQ)AAI31848673
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aHalavati, Aria.
■24510▼aThe Magnetic Ginzburg-Landau Equation: Stability, Regularity and Rigidity
■260 ▼a[Sl]▼bNew York University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a249 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: De Philippis, Guido;Lin, Fang-Hua.
■5021 ▼aThesis (Ph.D.)--New York University, 2025.
■520 ▼aWe study the magnetic Ginzburg-Landau energy in the critical coupling, also known as the abelian--Higgs model. It is known that entire solutions of the abelian-Higgs model blow down to (generalized) minimal submanifolds. We show that, in the so-called multiplicity one regime, critical points inherit an improvement of flatness and a rigidity property from their blow-down limit.This thesis consists of three parts. In the first two parts we develop the necessary toolbox for part three.First (in [44]), we develop a new class of weighted inequalities on any two-manifold (with boundary). Second (in [45]), using these inequalities and a selection principle (inspired by the quantitative isoperimetric inequality) we prove a sharp quantitative stability for the abelian-Higgs model in two dimensions.Third, (in a collaboration with Guido De Philippis and Alessandro Pigati in [28]) we leverage these tool to develop a large scale regularity theory for the zero set of solutions (in the spirit of Allard's). In fact, in the multiplicity one regime we show the uniqueness of blowdowns. Then we classify solutions in dimensions n 2.
■590 ▼aSchool code: 0146.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aApplied mathematics
■653 ▼aAbelian-Higgs model
■653 ▼aCalculus of variations
■653 ▼aGeometric measure theory
■653 ▼aGinzburg-Landau energy
■653 ▼aPartial differential equations
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aNew York University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0146
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356830▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
