Paper · Apr 16, 2020
On the nonexistence of harmonic and bi-harmonic maps
As on arXiv
Abstract
In this paper, we study the existence of harmonic and bi-harmonic maps into Riemannian manifolds admitting a conformal vector field, or a nontrivial Ricci solitons.
- Submitted
- Apr 16, 2020
- Subjects
- math.DG
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.
-
On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry
Topics Harmonic maps & DeTurck trick, Ricci solitons · Same author Ahmed Mohammed Cherif · Shared terms “vector field”, “Riemannian manifold”
-
On the stability of harmonic maps under the homogeneous Ricci flow
Topics Harmonic maps & DeTurck trick
-
Ricci Solitons on the Lie Group and Applications
Topics Harmonic maps & DeTurck trick, Ricci solitons · Same author Ahmed Mohammed Cherif · Shared terms “vector field”
-
On the non-existence of symphonic maps
Topics Ricci solitons · Same author Ahmed Mohammed Cherif · Shared terms “conformal vector”, “manifold admitting”, “Riemannian manifold”
-
Short time existence for harmonic map heat flow with time-dependent metrics
Topics Harmonic maps & DeTurck trick
-
On harmonic and biharmonic maps from gradient Ricci solitons
Topics Harmonic maps & DeTurck trick, Ricci solitons
-
Rigidity of Lipschitz map using harmonic map heat flow
Topics Harmonic maps & DeTurck trick
-
Mean curvature flow into an ambient Riemannian manifold evolving by Ricci flow coupled with harmonic map heat flow
Topics Harmonic maps & DeTurck trick, Ricci solitons · Shared terms “Riemannian manifold”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.