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arXiv · 2107.14686

Smoothing a measure on a Riemann surface using Ricci flow

Peter M. Topping·Hao Yin
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Abstract

We formulate and solve the existence problem for Ricci flow on a Riemann surface with initial data given by a Radon measure as volume measure. The theory leads us to a large class of new examples of nongradient expanding Ricci solitons, including the first example of a nongradient Kaehler Ricci soliton. It also settles the question of whether a smooth flow for positive time that attains smooth initial data in a distance metric sense must be smooth down to the initial time. We disprove this by giving an example of a complete Ricci flow starting with the Euclidean plane that is not the static solution.

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Peter M. Topping, Hao Yin. 2021-07-30. Smoothing a measure on a Riemann surface using Ricci flow. https://doi.org/10.15781/4x5c-9q97

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