Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 17 |
| Seitenumfang | 13 |
| Fachzeitschrift | Calculus of Variations and Partial Differential Equations |
| Jahrgang | 62 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 5 Nov. 2022 |
| Publikationsstatus | Veröffentlicht - Jan. 2023 |
Abstract
We relate the existence problem of harmonic maps into S2 to the convex geometry of S2. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into S2. On the other hand, we produce new examples of regions that do not contain closed geodesics (that is, harmonic maps from S1) but do contain images of harmonic maps from other domains. These regions can therefore not support a strictly convex functions. Our construction uses M. Struwe’s heat flow approach for the existence of harmonic maps from surfaces.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Calculus of Variations and Partial Differential Equations, Jahrgang 62, Nr. 1, 17, 01.2023.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Harmonic maps from surfaces of arbitrary genus into spheres
AU - Assimos, Renan
AU - Jost, Jürgen
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL.
PY - 2023/1
Y1 - 2023/1
N2 - We relate the existence problem of harmonic maps into S2 to the convex geometry of S2. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into S2. On the other hand, we produce new examples of regions that do not contain closed geodesics (that is, harmonic maps from S1) but do contain images of harmonic maps from other domains. These regions can therefore not support a strictly convex functions. Our construction uses M. Struwe’s heat flow approach for the existence of harmonic maps from surfaces.
AB - We relate the existence problem of harmonic maps into S2 to the convex geometry of S2. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into S2. On the other hand, we produce new examples of regions that do not contain closed geodesics (that is, harmonic maps from S1) but do contain images of harmonic maps from other domains. These regions can therefore not support a strictly convex functions. Our construction uses M. Struwe’s heat flow approach for the existence of harmonic maps from surfaces.
UR - http://www.scopus.com/inward/record.url?scp=85141438417&partnerID=8YFLogxK
U2 - 10.1007/s00526-022-02314-4
DO - 10.1007/s00526-022-02314-4
M3 - Article
AN - SCOPUS:85141438417
VL - 62
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
M1 - 17
ER -