curves on surfaces were first studied by Charles Loewner in 1949 (unpublished; see remark at end of P. M. Pu's paper in '52). Given a closed surface, its systole...

More details appear at systoles of surfaces. The deepest result in the field is Gromov's inequality for the homotopy 1-systole of an essential n-manifold...

term used in mathematics In mathematics, Systoles of surfaces are systolic inequalities for curves on surfaces Also see Introduction to systolic geometry...

Filling radius Filling area conjecture Bolza surface First Hurwitz triplet Hermite constant Systoles of surfaces Systolic freedom Systolic category Envelope...

geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have...

the symmetry group for surfaces of genus 3, it does not maximise the systole length. The conjectured maximiser is the surface referred to as "M3" (Schmutz...

a tight asymptotic bound for the systolic ratio of surfaces of large genus, see systoles of surfaces. Besson, G., Courtois, G., Gallot, S. Entropies et...

for the variance and Fubini's theorem (see Horowitz et al, 2009). Systoles of surfaces Sub-Riemannian geometry Bangert, V.; Croke, C.; Ivanov, S.; Katz...

are available for surfaces, where the asymptotics when the genus tends to infinity are by now well understood, see systoles of surfaces. A uniform inequality...

complex projective space Eisenstein integer (an example of a hexagonal lattice) Systoles of surfaces Horowitz, Charles; Katz, Karin Usadi; Katz, Mikhail G...