Convex valuation theory and integral geometry

凸几何是一个经典的，但发展迅速的数学分支，以各种形式出现在各种数学学科中，从代数和辛几何，到概率论和组合学，再到算法。积分几何在19世纪以多种形式出现。它与微分几何的区别在于研究全局不变量（如总长度），而不是局部不变量（如曲率）。

Convex geometry is a classical, yet rapidly developing branch of mathematics, appearing in various guises in a great variety of mathematical disciplines, ranging from algebraic and symplectic geometry, through probability theory and combinatorics, and on to algorithmics. Integral geometry appeared in the nineteenth century in several flavors. It distinguishes itself from differential geometry by studying global invariants (such as total length), rather than local invariants (such as curvature).