@article {2021, title = {The sharp quantitative isocapacitary inequality}, journal = {Revista Matematica Iberoamericana}, volume = {37}, year = {2021}, month = {2021}, pages = {2191 - 2228}, abstract = {

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.{\textquoteright}91). {\textcopyright} 2021 Real Sociedad Matem{\'a}tica Espa{\~n}ola

}, keywords = {Fraenkel asymmetry, isocapacitary inequality, Stability estimates}, isbn = {02132230 (ISSN)}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573\&doi=10.4171\%2frmi\%2f1259\&partnerID=40\&md5=5f88bc37b87a9eea7a502ea63523ff57}, author = {Guido De Philippis and Michele Marini and Ekaterina Mukoseeva} } @booklet {2019, title = {Regularity of minimizers for a model of charged droplets}, year = {2019}, author = {Guido De Philippis and Jonas Hirsch and Giulia Vescovo} } @article {2017arXiv170707595A, title = {The injectivity radius of Lie manifolds}, journal = {ArXiv e-prints}, year = {2017}, abstract = {

We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

}, keywords = {(58J40), 53C21, Mathematics - Differential Geometry}, url = {https://arxiv.org/pdf/1707.07595.pdf}, author = {Paolo Antonini and Guido De Philippis and Nicola Gigli} }