Systolic Geometry and Topology (Hardcover)

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