@article {2021,
	title = {A Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications},
	volume = {31},
	year = {2021},
	month = {2021/12/01},
	pages = {11780 - 11818},
	abstract = {<p>We review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on $$\textsf {CAT} (\kappa )$$-spaces and prove that they can be characterized by the same differential inclusion $$y_t{\textquoteright}\in -\partial ^-\textsf {E} (y_t)$$one uses in the smooth setting and more precisely that $$y_t{\textquoteright}$$selects the element of minimal norm in $$-\partial ^-\textsf {E} (y_t)$$. This generalizes previous results in this direction where the energy was also assumed to be Lipschitz. We then apply such result to the Korevaar{\textendash}Schoen energy functional on the space of $$L^2$$and CAT(0) valued maps: we define the Laplacian of such $$L^2$$map as the element of minimal norm in $$-\partial ^-\textsf {E} (u)$$, provided it is not empty. The theory of gradient flows ensures that the set of maps admitting a Laplacian is $$L^2$$-dense. Basic properties of this Laplacian are then studied.</p>},
	isbn = {1559-002X},
	url = {https://doi.org/10.1007/s12220-021-00701-5},
	author = {Nicola Gigli and Francesco Nobili}
}
@article {2021,
	title = {Displacement convexity of Entropy and the distance cost Optimal Transportation},
	journal = {Annales de la Facult{\'e} des sciences de Toulouse : Math{\'e}matiques},
	volume = {Ser. 6, 30},
	year = {2021},
	pages = {411{\textendash}427},
	doi = {10.5802/afst.1679},
	url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1679/},
	author = {Fabio Cavalletti and Nicola Gigli and Flavia Santarcangelo}
}
@article {GIGLI2019,
	title = {Differential structure associated to axiomatic Sobolev spaces},
	journal = {Expositiones Mathematicae},
	year = {2019},
	abstract = {<p>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.</p>},
	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 {1807.10063,
	title = {Differential of metric valued Sobolev maps},
	year = {2018},
	author = {Nicola Gigli and Enrico Pasqualetto and Elefterios Soultanis}
}
