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math.AP2014★ 22 cited
Slowly converging Yamabe flows
Alessandro Carlotto, Otis Chodosh, Yanir A. Rubinstein
We characterize the rate of convergence of a converging volume-normalized Yamabe flow in terms of Morse theoretic properties of the limiting metric. If the limiting metric is an in…
math.AP2011
On the solvability of singular Liouville equations on compact surfaces on arbitrary genus
Alessandro Carlotto
In the first part of this article, we complete the program announced in the preliminary note [8] by proving a conjecture presented in [9] that states the equivalence of contractibi…
math.AP2011
Weighted Barycentric Sets and Singular Liouville Equations on Compact Surfaces
Alessandro Carlotto, Andrea Malchiodi
Given a closed two dimensional manifold, we prove a general existence result for a class of elliptic PDEs with exponential nonlinearities and negative Dirac deltas on the right-han…