Journal article
A Sobolev gradient flow for the area-normalised Dirichlet energy of H1 maps
Advances in calculus of variations
2025
Abstract
In this article we study the H1-gradient flow for the energy E[X] given by the quotient of the Dirichlet energy and the signed enclosed area of an H1 map X : S -> R2. We prove that solutions with initially positive signed enclosed area exist eternally, and converge as t -> infinity to a (possibly multiply-covered) circle. In this way we recover an improved parametrised isoperimetric inequality for H1 maps.
Details
- Title
- A Sobolev gradient flow for the area-normalised Dirichlet energy of H1 maps
- Authors/Creators
- Shinya Okabe - Tohoku UniversityPhilip Schrader - Murdoch Univ, Sch Math & Stat Chem & Phys, South St, Murdoch, WA 6150, AustraliaGlen Wheeler - University of WollongongValentina-Mira Wheeler - University of Wollongong
- Publication Details
- Advances in calculus of variations
- Publisher
- Walter De Gruyter
- Number of pages
- 20
- Grant note
- 20KK0057; 21H00990 / Japan Society for the Promotion of Science; Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) JSPS KAKENHI; Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT); Japan Society for the Promotion of Science; Grants-in-Aid for Scientific Research (KAKENHI)
- Identifiers
- 991005812249307891
- Copyright
- © 2025 De Gruyter Brill
- Murdoch Affiliation
- School of Mathematics, Statistics, Chemistry and Physics
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.415 Harmonic Maps
- Web Of Science research areas
- Mathematics
- Mathematics, Applied
- ESI research areas
- Mathematics