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Найдено 16 публикаций
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Статья
Kolesnikov A., Milman E. Journal of Geometric Analysis. 2017. Vol. 27. No. 2. P. 1680-1702.

It is known that by dualizing the Bochner–Lichnerowicz–Weitzenböck formula, one obtains Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy the Bakry–Émery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an upper bound on its generalized dimension). When the manifold has a boundary, an appropriate generalization of the Reilly formula may be used instead. By systematically dualizing this formula for various combinations of boundary conditions of the domain (convex, mean-convex) and the function (Neumann, Dirichlet), we obtain new Brascamp–Lieb-type inequalities on the manifold. All previously known inequalities of Lichnerowicz, Brascamp–Lieb, Bobkov–Ledoux, and Veysseire are recovered, extended to the Riemannian setting and generalized into a single unified formulation, and their appropriate versions in the presence of a boundary are obtained. Our framework allows to encompass the entire class of Borell’s convex measures, including heavy-tailed measures, and extends the latter class to weighted-manifolds having negative generalized dimension.

Добавлено: 11 ноября 2016
Статья
Cheltsov Ivan, Kosta D. Journal of Geometric Analysis. 2014. Vol. 24. No. October. P. 798-842.

We prove a new local inequality for divisors on surfaces and utilize it to compute α-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type A1 , A2 , A3 , A4 , A5 , or A6 are Kähler-Einstein.

Добавлено: 14 ноября 2013
Статья
Cheltsov Ivan, Wilson A. Journal of Geometric Analysis. 2013. Vol. 23. No. 3. P. 1257-1289.

Del Pezzo surface Fano manifold Alpha-invariant of Tian Kähler–Einstein metric Kähler–Ricci iterations Automorphisms

Добавлено: 14 ноября 2013
Статья
Cheltsov I., Park J., Shramov K. Journal of Geometric Analysis. 2020.
Добавлено: 10 мая 2020
Статья
Cheltsov I., Park J., Shramov K. Journal of Geometric Analysis. 2010. No. 20. P. 787-816.
Добавлено: 28 февраля 2011
Статья
Klartag B., Kolesnikov A. Journal of Geometric Analysis. 2019. Vol. 29. No. 3. P. 2347-2373.
Добавлено: 1 сентября 2018
Статья
Penskoi A. Journal of Geometric Analysis. 2015. Vol. 25. No. 4. P. 2645-2666.
Добавлено: 11 марта 2016
Статья
Isozaki H., Korotyaev Evgeny. Journal of Geometric Analysis. 2020. Vol. 30. P. 4427-4452.

We consider an inverse problem for Laplacians on rotationally symmetric  manifolds, which are finite  for the transversal direction and periodic with respect to the axis of the manifold, i.e.,  Laplacians on tori.  We construct an infinite dimensional analytic isomorphism between the space of profiles  (the radius of the rotation) of the torus and the spectral data as well as the stability estimates: those for the spectral data in terms of the profile and conversely, for the profile in term of the spectral data.

Добавлено: 5 февраля 2021
Статья
Kolesnikov A., Barthe F. Journal of Geometric Analysis. 2008. No. 18 (4). P. 921-979.
Добавлено: 23 марта 2011
Статья
Glutsyuk A. Journal of Geometric Analysis. 2017. Vol. 27. No. 1. P. 183-238.
Добавлено: 2 ноября 2016
Статья
Kolesnikov A., Livshyts G., Hosle J. Journal of Geometric Analysis. 2020.

We study several of the recent conjectures in regards to the role of symmetry in the inequalities of Brunn-Minkowski type, such as the Lp-Brunn-Minkowski conjecture of Böröczky, Lutwak, Yang and Zhang, and the Dimensional Brunn-Minkowski conjecture of Gardner and Zvavitch, in a unified framework. We obtain several new results for these conjectures. We show that when K⊂L, the multiplicative form of the Lp-Brunn-Minkowski conjecture holds for Lebesgue measure for p≥1−Cn−0.75, which improves upon the estimate of Kolesnikov and Milman in the partial case when one body is contained in the other. We also show that the multiplicative version of the Lp-Brunn-Minkowski conjecture for the standard Gaussian measure holds in the case of sets containing sufficiently large ball (whose radius depends on p). In particular, the Gaussian Log-Brunn-Minkowski conjecture holds when K and L contain 0.5(n+1)−−−−−−−−√Bn2. We formulate an a-priori stronger conjecture for log-concave measures, extending both the Lp-Brunn-Minkowski conjecture and the Dimensional one, and verify it in the case when the sets are dilates and the measure is Gaussian. We also show that the Log-Brunn-Minkowski conjecture, if verified, would yield this more general family of inequalities. Our results build up on the methods developed by Kolesnikov and Milman as well as Colesanti, Livshyts, Marsiglietti. We furthermore verify that the local version of these conjectures implies the global version in the setting of general measures, and this step uses methods developed recently by Putterman

Добавлено: 4 февраля 2021
Статья
Alesker S., Verbitsky M. Journal of Geometric Analysis. 2006. Vol. 16. No. 3. P. 375-399.
Добавлено: 2 ноября 2010
Статья
Ornea L., Verbitsky M. Journal of Geometric Analysis. 2019. Vol. 29. No. 2. P. 1479-1489.
Добавлено: 11 октября 2019
Статья
Baranov A., Dyakonov К. Journal of Geometric Analysis. 2011. No. 2. P. 276-287.
Добавлено: 17 января 2014
Статья
Eugene Stepanov, Trevisan D. Journal of Geometric Analysis. 2020.
Добавлено: 14 октября 2020
Статья
Cheltsov I. Journal of Geometric Analysis. 2017.

We prove that (Formula presented.) and (Formula presented.) are the smallest log canonical thresholds of reduced plane curves of degree (Formula presented.), and we describe reduced plane curves of degree d whose log canonical thresholds are these numbers. As an application, we prove that (Formula presented.) and (Formula presented.) are the smallest values of the (Formula presented.)-invariant of Tian of smooth surfaces in (Formula presented.) of degree (Formula presented.). We also prove that every reduced plane curve of degree (Formula presented.) whose log canonical threshold is smaller than (Formula presented.) is GIT-unstable for the action of the group (Formula presented.), and we describe GIT-semistable reduced plane curves with log canonical thresholds (Formula presented.).

Добавлено: 14 марта 2017