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We prove that the Bourgain slicing conjecture and the Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture in $\mathbb{R}^n$ hold true up to a factor of $\sqrt{\log n}$.
Bobkov, S. G., Isoperimetric and analytic inequalities for log-concave probability measures
1921
Earlier work this paper cites.
Grünbaum, B., Partitions of mass-distributions and of convex bodies by hyperplanes
1960
Earlier work this paper cites.
Cheeger, J., A lower bound for the smallest eigenvalue of the Laplacian
1970
Earlier work this paper cites.
Combes, J. M., Thomas, L., Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
1973
Earlier work this paper cites.
O’Connor, A. J., Exponential decay of bound state wave functions
1973
Earlier work this paper cites.
Brascamp, H. J., Lieb, E. H., On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
1976
Earlier work this paper cites.
Carmona, R., Pointwise bounds for Schrödinger eigenstates
1978
Earlier work this paper cites.
Hensley, D., Slicing convex bodies—bounds for slice area in terms of the body’s covariance
1980
Earlier work this paper cites.
Agmon, S., Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N 𝑁 N italic_N -body Schrödinger operators
1982
Earlier work this paper cites.
Buser, P., A note on the isoperimetric constant
1982
Earlier work this paper cites.
Bourgain, J., On the distribution of polynomials on high dimensional convex sets
1991
Earlier work this paper cites.
Kannan, R., Lovász, L., Simonovits M., Isoperimetric problems for convex bodies and a localization lemma
1995
Earlier work this paper cites.
Fradelizi, M., Hyperplane sections of convex bodies in isotropic position
1999
Earlier work this paper cites.
Ledoux, M., The concentration of measure phenomenon
2001
Cited alongside, same era.
Bourgain, J., On the isotropy-constant problem for “Psi- 2 2 2 2 ” bodies
2002
Cited alongside, same era.
Ledoux, M., Spectral gap, logarithmic Sobolev constant, and geometric bounds
2004
Cited alongside, same era.
Chiganski, P., Introduction to Nonlinear Filtering
2005
Cited alongside, same era.
Klartag, B., On convex perturbations with a bounded isotropic constant
2006
Cited alongside, same era.
Klartag, B., A Berry-Esseen type inequality for convex bodies with an unconditional basis
2009
Cited alongside, same era.
Brazitikos, S., Giannopoulos, A., Valettas, P., Vritsiou, B. -H., Geometry of isotropic convex bodies
2014
Later among the works it cites.
Nguyen, V. H., Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prékopa’s theorem
2014
Later among the works it cites.
Lee, Y. T., Vempala, S., Eldan’s Stochastic Localization and the KLS Conjecture: Isoperimetry, Concentration and Mixing
2017
Later among the works it cites.
Klartag, B., Needle decompositions in Riemannian geometry
2017
Later among the works it cites.
Barthe, F., Klartag, B., Spectral gaps, symmetries and log-concave perturbations
2020
Later among the works it cites.
Courtade, T. A., Bounds on the Poincaré constant for convolution measures
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Milman, E., On the role of convexity in isoperimetry, spectral gap and concentration
2009
Cited alongside, same era.
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2010
Cited alongside, same era.
Bobkov S.G., Madiman, M., Concentration of the information in data with logconcave distributions
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Cited alongside, same era.
Eldan, R., Klartag, B., Approximately Gaussian marginals and the hyperplane conjecture
2011
Cited alongside, same era.
Ball, K., Nguyen, V. H., Entropy jumps for isotropic log-concave random vectors and spectral gap
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Cited alongside, same era.
Eldan, R., Thin shell implies spectral gap via a stochastic localization scheme
2013
Cited alongside, same era.
2020
Later among the works it cites.
Judge, C., Mondal, S., Euclidean triangles have no hot spots
2020
Later among the works it cites.
Chen, Y., An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture
2021
Later among the works it cites.
Klartag, B., On Yuansi Chen’s work on the KLS conjecture
2021
Later among the works it cites.
Klartag, B., Lehec, J., Bourgain’s slicing problem and KLS isoperimetry up to polylog
2022
Later among the works it cites.
Klartag, B., Milman, V., The slicing problem by Bourgain
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Later among the works it cites.
Reed, M., Simon, B., Methods of modern mathematical physics. IV. Analysis of operators
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