@booklet {2021, title = {On master test plans for the space of BV functions}, year = {2021}, author = {Francesco Nobili and Enrico Pasqualetto and Timo Schultz} } @booklet {2021, title = {Parallel transport on non-collapsed $\mathsfRCD(K,N)$ spaces}, year = {2021}, abstract = {

We provide a general theory for parallel transport on non-collapsed\ RCD\ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regular time dependent vector fields: the price that we pay for this generality is that we cannot study parallel transport along a single such curve, but only along almost all of these (in a sense related to the notions of Sobolev vector calculus and Regular Lagrangian Flow in the nonsmooth setting).
The class of\ ncRCD\ spaces contains finite dimensional Alexandrov spaces with curvature bounded from below, thus our construction provides a way of speaking about parallel transport in this latter setting alternative to the one proposed by Petrunin (1998). The precise relation between the two approaches is yet to be understood.

}, author = {Emanuele Caputo and Nicola Gigli and Enrico Pasqualetto} } @article {GIGLI2019, title = {Differential structure associated to axiomatic Sobolev spaces}, journal = {Expositiones Mathematicae}, year = {2019}, abstract = {

The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space ({\`a} la Gol{\textquoteright}dshtein{\textendash}Troyanov) induces {\textendash} under suitable locality assumptions {\textendash} a first-order differential structure.

}, keywords = {Axiomatic Sobolev space, Cotangent module, Locality of differentials}, issn = {0723-0869}, doi = {https://doi.org/10.1016/j.exmath.2019.01.002}, url = {http://www.sciencedirect.com/science/article/pii/S0723086918300975}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {1903.04302, title = {Quasi-continuous vector fields on RCD spaces}, year = {2019}, author = {Cl{\'e}ment Debin and Nicola Gigli and Enrico Pasqualetto} } @article {Lu{\v c}i{\'c}2019, title = {The Serre{\textendash}Swan theorem for normed modules}, journal = {Rendiconti del Circolo Matematico di Palermo Series 2}, volume = {68}, number = {2}, year = {2019}, month = {Aug}, pages = {385{\textendash}404}, issn = {1973-4409}, doi = {10.1007/s12215-018-0366-6}, url = {https://doi.org/10.1007/s12215-018-0366-6}, author = {Danka Lu{\v c}i{\'c} and Enrico Pasqualetto} } @article {1807.10063, title = {Differential of metric valued Sobolev maps}, year = {2018}, author = {Nicola Gigli and Enrico Pasqualetto and Elefterios Soultanis} } @article {1803.05374, title = {On the notion of parallel transport on RCD spaces}, year = {2018}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {1607.05188, title = {Behaviour of the reference measure on RCD spaces under charts}, year = {2016}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {1611.09645, title = {Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces}, year = {2016}, author = {Nicola Gigli and Enrico Pasqualetto} }