Work

Geometric and analytical results for ρ‐Einstein solitons

Year: 2025

Type: article

Abstract: In this paper, we study geometric and analytical features of complete noncompact ‐Einstein solitons, which are self‐similar solutions of the Ricci–Bourguignon flow. We study the spectrum of the drifted Laplacian operator for complete gradient shrinking ‐Einstein solitons. Moreover, similar to classical results due to Calabi–Yau and Bishop for complete Riemannian manifolds with nonnegative Ricci curvature, we prove new volume growth estimates for geodesic balls of complete noncompact ‐Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70084

Author: Caio Coimbra

Institution: Universidade Federal do Ceará

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Award: G29316538