147 citations · 365 across the 33 of their papers we have counts for
6 papers · 1 filter
Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces
Peter M. Topping, Hao Yin
We prove the sharp local L^1 - L^\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instant…
Ricci flows with bursts of unbounded curvature
Gregor Giesen, Peter M. Topping
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution…
Ricci flows with unbounded curvature
Gregor Giesen, Peter M. Topping
We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).
Decay estimates for Rivière's equation, with applications to regularity and compactness
Ben Sharp, Peter Topping
We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in introduced by Rivière. Applications include sharp regularit…
Existence of Ricci flows of incomplete surfaces
Gregor Giesen, Peter M. Topping
We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. W…
Ricci flow of negatively curved incomplete surfaces
Gregor Giesen, Peter M. Topping
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more…