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p-Weak differentiable structures

Elefterios Soultanis
Tuesday, May 11, 2021 - 11:30

Combining the modulus and plan approaches to Sobolev spaces on metric measure spaces yields a representation of minimal weak upper gradients as maximal directional derivatives along generic curves. In this talk I explain how this result can be used to extract geometric information of the underlying space and define a p-weak differentiable structure (with an associated differential for Sobolev functions), in the spirit of the seminal work of Cheeger. This structure coincides with Cheeger's differentiable structure on PI-spaces, and is also compatible with Gigli's cotangent module. The talk is based on joint work with S. Eriksson-Bique. 

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