Sequences of Laplacian cut-off functions

2014/01/16 by Batu Güneysu, Güneysu, Batu · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1401.4036

openalex publication_date 2014/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular, we prove that this existence implies L^q-estimates of the gradient, a new density result of smooth compactly supported functions in Sobolev spaces on the whole L^q-scale, and a slightly weaker and slightly stronger variant of the conjecture of Braverman, Milatovic and Shubin on the nonnegativity of L²-solutions f of (-Δ+1)f≥ 0. The latter fact is proved within a new notion of positivity preservation for Riemannian manifolds which is related to stochastic completeness.

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