Abstract
Abstract We prove Łojasiewicz inequalities for round cylinders and cylinders over Abresch–Langer curves, using perturbative analysis of a quantity introduced by Colding–Minicozzi. A feature is that this auxiliary quantity allows us to work essentially at 1st order. This new method interpolates between the higher-order perturbative analysis used by the author for certain shrinking cylinders and the differential geometric method used by Colding–Minicozzi for the round case.
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