Weak solutions of Ricci Flow, and how uniqueness can fail
October 26, 2022
3:00 pm PGH 646 (in person)
Abstract
In dimensions 2 and 3 (and in higher dimensions with some
restrictions), there are complete theories of weak solutions that
provide canonical evolutions of the Ricci Flow initial value problem.
We will introduce these and discuss how, in dimensions 5 and above,
uniqueness cannot be expected to hold. Specifically, we will show that
in these dimensions, there exist smooth complete initial metrics whose
forward evolutions under Ricci Flow are not unique after a first
singularity forms, and whose topology may change at the singularity
for some solutions but not for others.
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Last modified: April 11 2016 - 18:14:43