Growth conditions for conformal transformations preserving Riemannian completeness

2012/02/24 by Alexander Dirmeier, Dirmeier, A.
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1202.5437

openalex publication_date 2012/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conformally transformed Riemannian metric remains complete.

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