Local minimality of the ball for the Gaussian perimeter

References

[1] E. Acerbi, N. Fusco and M. Morini, Minimality via second variation for a nonlocal isoperimetric problem, Comm. Math. Phys. 322 (2013), no. 2, 515–557. 10.1007/s00220-013-1733-ySearch in Google Scholar

[2] L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Math. Monogr., Clarendon Press, New York, 2000. 10.1093/oso/9780198502456.001.0001Search in Google Scholar

[3] M. Barchiesi, A. Brancolini and V. Julin, Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality, Ann. Probab. 45 (2017), no. 2, 668–697. 10.1214/15-AOP1072Search in Google Scholar

[4] F. Barthe, An isoperimetric result for the Gaussian measure and unconditional sets, Bull. Lond. Math. Soc. 33 (2001), no. 4, 408–416. 10.1017/S0024609301008141Search in Google Scholar

[5] V. Bögelein, F. Duzaar and N. Fusco, A sharp quantitative isoperimetric inequality in higher codimension, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 3, 309–362. 10.4171/RLM/709Search in Google Scholar

[6] V. Bögelein, F. Duzaar and N. Fusco, A quantitative isoperimetric inequality on the sphere, Adv. Calc. Var. 10 (2017), no. 3, 223–265. 10.1515/acv-2015-0042Search in Google Scholar

[7] C. Borell, The Brunn–Minkowski inequality in Gauss space, Invent. Math. 30 (1975), no. 2, 207–216. 10.1007/BF01425510Search in Google Scholar

[8] L. Brasco, G. De Philippis and B. Velichkov, Faber–Krahn inequalities in sharp quantitative form, Duke Math. J. 164 (2015), no. 9, 1777–1831. 10.1215/00127094-3120167Search in Google Scholar

[9] E. A. Carlen and C. Kerce, On the cases of equality in Bobkov’s inequality and Gaussian rearrangement, Calc. Var. Partial Differential Equations 13 (2001), no. 1, 1–18. 10.1007/PL00009921Search in Google Scholar

[10] A. Chakrabarti and O. Regev, An optimal lower bound on the communication complexity of gap-Hamming-distance, STOC’11 – Proceedings of the 43rd ACM Symposium on Theory of Computing, ACM, New York (2011), 51–60. 10.1145/1993636.1993644Search in Google Scholar

[11] A. Cianchi, N. Fusco, F. Maggi and A. Pratelli, On the isoperimetric deficit in Gauss space, Amer. J. Math. 133 (2011), no. 1, 131–186. 10.1353/ajm.2011.0005Search in Google Scholar

[12] M. Cicalese and G. P. Leonardi, A selection principle for the sharp quantitative isoperimetric inequality, Arch. Ration. Mech. Anal. 206 (2012), no. 2, 617–643. 10.1007/s00205-012-0544-1Search in Google Scholar

[13] R. Eldan, A two-sided estimate for the Gaussian noise stability deficit, Invent. Math. 201 (2015), no. 2, 561–624. 10.1007/s00222-014-0556-6Search in Google Scholar

[14] N. Fusco, The quantitative isoperimetric inequality and related topics, Bull. Math. Sci. 5 (2015), no. 3, 517–607. 10.1007/s13373-015-0074-xSearch in Google Scholar

[15] N. Fusco and V. Julin, A strong form of the quantitative isoperimetric inequality, Calc. Var. Partial Differential Equations 50 (2014), no. 3–4, 925–937. 10.1007/s00526-013-0661-1Search in Google Scholar

[16] N. Fusco, F. Maggi and A. Pratelli, The sharp quantitative isoperimetric inequality, Ann. of Math. (2) 168 (2008), no. 3, 941–980. 10.4007/annals.2008.168.941Search in Google Scholar

[17] S. Heilman, Low correlation noise stability of symmetric sets, preprint (2016), https://arxiv.org/abs/1511.00382v4. 10.1007/s10959-020-01031-ySearch in Google Scholar

[18] S. Heilman, Symmetric convex sets with minimal Gaussian surface area, preprint (2017), https://arxiv.org/abs/1705.06643v1. 10.1353/ajm.2021.0000Search in Google Scholar

[19] F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems, Cambridge Stud. Adv. Math. 135, Cambridge University Press, Cambridge, 2012. 10.1017/CBO9781139108133Search in Google Scholar

[20] E. Mossel and J. Neeman, Robust dimension free isoperimetry in Gaussian space, Ann. Probab. 43 (2015), no. 3, 971–991. 10.1214/13-AOP860Search in Google Scholar

[21] E. Mossel, R. O’Donnell and K. Oleszkiewicz, Noise stability of functions with low influences: Invariance and optimality, Ann. of Math. (2) 171 (2010), no. 1, 295–341. 10.4007/annals.2010.171.295Search in Google Scholar

[22] R. O’Donnell, Analysis of Boolean Functions, Cambridge University Press, New York, 2014. 10.1017/CBO9781139814782Search in Google Scholar

[23] V. N. Sudakov and B. S. Cirel’son, Extremal properties of half-spaces for spherically invariant measures, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 41 (1974), 14–24, 165. 10.1007/BF01086099Search in Google Scholar

[24] I. Tamanini, Regularity Results for Almost Minimal Oriented Hypersurfaces, Quaderni del Dipartimento di Matematica dell’Università di Lecce, Lecce, 1984; see also http://cvgmt.sns.it/paper/1807/. Search in Google Scholar