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Найдено 14 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
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
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