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arXiv · 2412.14767

Geometric and analytical results for $\rho$-Einstein solitons

Caio Coimbra
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Abstract

In this article, we study geometric and analytical features of complete noncompact $\rho$-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 $\rho$-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 $\rho$-Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds.

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Caio Coimbra. 2024-12-19. Geometric and analytical results for $\rho$-Einstein solitons. https://arxiv.org/abs/2412.14767

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