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Isoperimetric Inequalities and Logarithmic Brunn-Minkowski Conjecture

ФИО студента: Galkin Artem

Руководитель: Alexander Kolesnikov

Кампус/факультет: Faculty of Mathematics

Программа: Mathematics (Bachelor)

Год защиты: 2018

Работа поделена на две части. В первой части рассматриваются неравенства стабильности для локального p-неравенства Брунна-Минковского и предлагается усиление неравенств стабильности для анизотропного изопериметрического неравенства. Вторая часть посвящена функциональным аналогам классической задачи Минковского. Предлагается вариационный подход для решения логарифмической проблемы Минковского при помощи оптимальной транспортировки.

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