Systolic geometry and topology

摘要: Systolic geometry in dimension 2: Geometry and topology of systoles Historical remarks The theorema egregium Gauss Global surfaces Inequalities Loewner Pu applications integral A primer on Filling area theorem for hyperelliptic Hyperelliptic are An optimal inequality CAT(0) metrics Volume entropy asymptotic upper bounds $n$ dimensions: Systoles their category Gromov's stable systolic $\mathbb{CP}^n$ inequalities dependent Massey products Cup Dual-critical lattices Generalized degree Loewner-type Higher Loewner-Gromov type $L^p$ norms Four-manifold systole asymptotics Period map image density (by Jake Solomon) Open problems Bibliography Index.