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Sharp local decay estimates for the Ricci flow on surfaces

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Sharp local decay estimates for the Ricci flow on surfaces
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6
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21
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CC Attribution 3.0 Unported:
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Abstract
There are many tools available when studying 2D Ricci flow, equivalently the logarithmic fast diffusion equation, but one has always been missing: how do you get uniform smoothing estimates in terms of local L^1 data, i.e. in terms of local bounds on the area. The problem is that the direct analogue of the geometrically less-useful L^p smoothing estimates for p bigger than 1 are simply false. In this talk I will explain this problem in more detail, and show how to get around it with a new local decay estimate. I also plan to sketch the proof and/or give some applications. No knowledge of Ricci flow will be assumed