Stephen Keith (Australian National University)
Differentiable structures for metric measure spaces
Abstract.
My talk will be structured around my thesis, the main result being the
provision of conditions under which a
metric measure
space admits a differentiable structure. This differentiable structure
gives rise to a finitedimensional
L_\infty cotangent bundle over the given metric measure space and then to
a
Sobolev
space H^{1,p} over the given metric measure space, the latter which is
reflexive for p>1: This
extends results of Cheeger (Geom. Funct. Anal. 9 (1999) (3) 428) to a
wider collection of
metric measure spaces.
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