论文标题
纳扎罗夫的非对称性波兰 - 米尔曼不平等现象
The Nazarov proof of the non-symmetric Bourgain--Milman inequality
论文作者
论文摘要
2012年，纳扎罗夫（Nazarov）使用了Bergman内核和Hormander的$ l^2 $估算值，$ \ bar \ partial $ - equation，给出了对称凸体的新证明 - 米尔曼定理，并就他的证明应如何扩展到一般凸面。本文实现了这一扩展，并同时使用了纳扎罗夫的作品。一个关键的新成分是与管域的伯格曼内核相关的仿射不变。这给出了普通凸体的首个Bourgain-Milman定理的第一个“复杂”证明，特别是无需使用对称。
In 2012, Nazarov used Bergman kernels and Hormander's $L^2$ estimates for the $\bar\partial$-equation to give a new proof of the Bourgain--Milman theorem for symmetric convex bodies and made some suggestions on how his proof should extend to general convex bodies. This article achieves this extension and serves simultaneously as an exposition to Nazarov's work. A key new ingredient is an affine invariant associated to the Bergman kernel of a tube domain. This gives the first `complex' proof of the Bourgain--Milman theorem for general convex bodies, specifically, without using symmetrization.
