We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A Note on the Critical Laplace Equation and Ricci Curvature.
- Authors
Fogagnolo, Mattia; Malchiodi, Andrea; Mazzieri, Lorenzo
- Abstract
We study strictly positive solutions to the critical Laplace equation - Δ u = n (n - 2) u n + 2 n - 2 , decaying at most like d (o , x) - (n - 2) / 2 , on complete noncompact manifolds (M, g) with nonnegative Ricci curvature, of dimension n ≥ 3 . We prove that, under an additional mild assumption on the volume growth, such a solution does not exist, unless (M, g) is isometric to R n and u is a Talenti function. The method employs an elementary analysis of a suitable function defined along the level sets of u.
- Subjects
MANIFOLDS (Mathematics); LEVEL set methods; RIEMANNIAN manifolds; DIFFERENTIAL geometry; EUCLIDEAN geometry
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 6, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-023-01223-y