arXiv subjects

Catalin C. Vasii

Publications and source records attributed to Catalin C. Vasii.

2 recordsLinked to original sources

arXiv2006

The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

In this paper it is proven that the volume entropy of a riemannian metric evolving by the Ricci flow, if does not collapse, nondecreases. Therefore, it provides a sufficient condition for a solution to collapse. Then, for the limit solutions of type I or III, the limit entropy is the limit of the entropy as $t$ approaches the singular (finite or not) time.

math.DG↗

arXiv2004

An ILB- Manifold Structure on the Set of Riemannian Metrics on a Noncompact Manifold

In this paper, using the structures of cone and bicone fields on vector bundles, the author introduces a ILB (inverse limit of Banach)- manifold structure on $\mathcal M$ the space of Riemannian metrics on a noncompact manifold $M$. In the last section, it is proven that, this way, on the open submanifold $\mathcal{M}_{finite}$ of finite volume metrics, the canonical Riemannian metric is defined.

math.DG↗