A lower bound for the scalar curvature of noncompact nonflat Ricci shrinkers

Abstract

We show that recent work of Ni and Wilking yields the result that a noncompact nonflat Ricci shrinker has at most quadratic scalar curvature decay. The examples of noncompact Kähler--Ricci shrinkers by Feldman, Ilmanen, and Knopf exhibit that this result is sharp.

arXiv comment2 pages

References in corpus (1)

• A compactness theorem for complete Ricci shrinkers

Cited by in corpus (3)

• Geometry of shrinking Ricci solitons
• Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons
• Uncertainty Principle and its rigidity on complete gradient shrinking Ricci solitons