TY - JOUR T1 - The sharp quantitative isocapacitary inequality JF - Revista Matematica Iberoamericana Y1 - 2021 A1 - Guido De Philippis A1 - Michele Marini A1 - Ekaterina Mukoseeva KW - Fraenkel asymmetry KW - isocapacitary inequality KW - Stability estimates AB -

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

VL - 37 SN - 02132230 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 IS - 6 JO - Rev. Mat. Iberoam. ER - TY - ABST T1 - Regularity of minimizers for a model of charged droplets Y1 - 2019 A1 - Guido De Philippis A1 - Jonas Hirsch A1 - Giulia Vescovo ER - TY - JOUR T1 - The injectivity radius of Lie manifolds JF - ArXiv e-prints Y1 - 2017 A1 - Paolo Antonini A1 - Guido De Philippis A1 - Nicola Gigli KW - (58J40) KW - 53C21 KW - Mathematics - Differential Geometry AB -

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

UR - https://arxiv.org/pdf/1707.07595.pdf ER -