Paper · Sep 30, 2016
Liouville-type theorems on the complete gradient shrinking Ricci solitons
As on arXiv
Abstract
We prove that there does not exist non-constant positive -harmonic function on the complete gradient shrinking Ricci solitons. We also prove the Liouville theorems on the complete gradient shrinking Ricci solitons.
- Submitted
- Sep 30, 2016
- Last revised
- Oct 9, 2016 (v2)
- Subjects
- math.DG
Comments: Add Example 0.8, some remarks and a reference
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.
-
Liouville type theorems for harmonic functions on gradient Ricci solitons
Topics Ricci solitons · Shared terms “Liouville type”, “type theorem”, “harmonic functions”
-
Three circles theorems and Liouville type theorems
Topics Ricci solitons · Shared terms “Liouville type”, “type theorem”, “gradient shrinking”
-
Liouville Theorem on Ricci shrinkers with constant scalar curvature and its application
Topics Ricci solitons · Shared terms “Liouville theorem”, “gradient shrinking”, “harmonic functions”
-
Liouville theorems for harmonic 1-forms on gradient Ricci solitons
Topics Ricci solitons · Shared terms “complete gradient”, “Liouville theorem”, “gradient shrinking”
-
Uncertainty Principle and its rigidity on complete gradient shrinking Ricci solitons
Topics Ricci solitons · Shared terms “complete gradient”, “shrinking Ricci”, “gradient shrinking”
-
Liouville theorems for pluriharmonic functions on gradient Kähler-Ricci solitons
Topics Ricci solitons · Shared terms “Liouville type”, “complete gradient”, “Liouville theorem”
-
A Liouville type theorem for ancient Lagrangian mean curvature flows
Shared terms “Liouville type”, “type theorem”
-
Four-dimensional complete gradient shrinking Ricci solitons
Topics Ricci solitons · Shared terms “complete gradient”, “gradient shrinking”, “shrinking Ricci”
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.