Ancient solutions to geometric flows
Ancient solutions to geometric flows
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Panagiota Daskalopoulos , Columbia University
We will discussÌý ancientÌýÌý or eternal solutions toÌý geometric parabolic partial differential equations. ÌýThese areÌý specialÌý solutions thatÌý appear as blow up limits near a singularity. They often representÌý models of ingularities. ÌýWe will addressÌý theÌý classification ofÌý ancientÌý solutions to geometric flows such as the Mean Curvature flow,Ìý the RicciÌý flow andÌý the Yamabe flow, as well as methods ofÌý constructing new ancient solutions fromÌý the gluing of two or more solitons. ÌýWe will also includeÌý futureÌý researchÌý directions.Ìý