naa a22 4500 510811124 CHVBK 20180411083443.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s12220-011-9270-4 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9270-4 A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones [Elektronische Daten] [A. Figalli, E. Indrei] The relative isoperimetric inequality inside an open, convex cone $\mathcal{C}$ states that, at fixed volume, $B_{r} \cap\mathcal{C}$ minimizes the perimeter inside $\mathcal{C}$ . Starting from the observation that this result can be recovered as a corollary of the anisotropic isoperimetric inequality, we exploit a variant of Gromov's proof of the classical isoperimetric inequality to prove a sharp stability result for the relative isoperimetric inequality inside $\mathcal{C}$ . Our proof follows the line of reasoning in Figalli et al.: Invent. Math. 182:167-211 (2010), though several new ideas are needed in order to deal with the lack of translation invariance in our problem. Mathematica Josephina, Inc., 2011 Relative isoperimetric inequality nationallicence Optimal transport nationallicence Sets of finite perimeter nationallicence Figalli A. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, 78712, Austin, TX, USA aut Indrei E. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, 78712, Austin, TX, USA aut Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 938-969 1050-6926 23:2<938 2013 23 12220 https://doi.org/10.1007/s12220-011-9270-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9270-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Figalli A. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, 78712, Austin, TX, USA aut NATIONALLICENCE 700 1- Indrei E. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, 78712, Austin, TX, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 938-969 1050-6926 23:2<938 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer