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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets II
无限维 凸紧集 混合体积
2023/11/6
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets I
无限维 凸紧集 混合体积
2023/11/6
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Differentiability of volume functions for big classes
大类 体积函数 可微性
2023/4/17
We report a recent paper of Witt Nystrom, where he proved the differentiability of volume functions using deformation to the normal cone.
VOLUME COMPARISON OF CONFORMALLY COMPACT MANIFOLDS WITH SCALAR CURVATURER≥ −n(n−1)
CONFORMALLY COMPACT MANIFOLDS called renormal-ized volume
2014/9/26
In this paper, we present a global invariant, called renormal-ized volume, which can be defined for a large class of conformally compact
manifolds. We use this definition to show a local volume compa...