01083nas a2200205 4500008004100000020002000041245005200061210004800113260000900161300001600170490000700186520039600193653002300589653002900612653002400641100002400665700002000689700002500709856014300734 2021 eng d a02132230 (ISSN)00aThe sharp quantitative isocapacitary inequality0 asharp quantitative isocapacitary inequality c2021 a2191 - 22280 v373 a
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.'91). © 2021 Real Sociedad Matemática Española
10aFraenkel asymmetry10aisocapacitary inequality10aStability estimates1 aDe Philippis, Guido1 aMarini, Michele1 aMukoseeva, Ekaterina uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff5700418nas a2200109 4500008004100000245006100041210006100102100002400163700001800187700002000205856008300225 2019 eng d00aRegularity of minimizers for a model of charged droplets0 aRegularity of minimizers for a model of charged droplets1 aDe Philippis, Guido1 aHirsch, Jonas1 aVescovo, Giulia uhttps://math.sissa.it/publication/regularity-minimizers-model-charged-droplets00713nas a2200157 4500008004100000245004400041210004000085520026500125653001200390653001000402653004000412100002000452700002400472700001800496856004100514 2017 eng d00aThe injectivity radius of Lie manifolds0 ainjectivity radius of Lie manifolds3 aWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive
10a(58J40)10a53C2110aMathematics - Differential Geometry1 aAntonini, Paolo1 aDe Philippis, Guido1 aGigli, Nicola uhttps://arxiv.org/pdf/1707.07595.pdf