Volume growth, ``a priori estimates, and geometric applications

DOI10.1007/s00039-003-0447-2zbMath1065.53037OpenAlexW2025853708MaRDI QIDQ1430516

Marco Rigoli, Alberto G. Setti, Stefano Pigola

Publication date: 27 May 2004

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-003-0447-2

zbMATH Keywords

maximum principle Schwarz lemma Liouville theorem geodesic ball a priori estimate volume growth complete Riemannian manifold Yamabe equation \(\varphi\)-Laplacian

Mathematics Subject Classification ID

PDEs with multivalued right-hand sides (35R70) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (21)

Geometries and topologies of conformally flat Riemannian manifolds ⋮ Lichnerowicz-type equations on complete manifolds ⋮ Qualitative properties for solutions of singular elliptic inequalities on complete manifolds ⋮ ``A priori estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds ⋮ \(L^2\) curvature pinching theorems and vanishing theorems on complete Riemannian manifolds ⋮ Volume growth for geodesic balls of static vacuum space on 3-manifolds ⋮ Maps from Riemannian manifolds into non-degenerate Euclidean cones ⋮ A barrier principle at infinity for varifolds with bounded mean curvature ⋮ Remarks on non-compact gradient Ricci solitons ⋮ A note on the volume growth criterion for stochastic completeness of weighted graphs ⋮ Spectral and stochastic properties of the \(f\)-Laplacian, solutions of PDEs at infinity and geometric applications ⋮ A priori upper bounds of solutions satisfying a certain differential inequality on complete manifolds ⋮ Existence and non-existence results for a logistic-type equation on manifolds ⋮ On the structure of conformally flat Riemannian manifolds ⋮ On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups ⋮ Some triviality results for quasi-Einstein manifolds and Einstein warped products ⋮ Non-existence of entire solutions of degenerate elliptic inequalities with weights ⋮ A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds ⋮ Default functions and Liouville type theorems based on symmetric diffusions ⋮ Some remarks on the weak maximum principle ⋮ Vanishing theorems on Riemannian manifolds, and geometric applications

This page was built for publication: Volume growth, ``a priori estimates, and geometric applications