Dyck's surfaces, systoles, and capacities
作者： Mikhail G. Katz , Stéphane Sabourau
DOI: 10.1090/S0002-9947-2014-06216-8
关键词: Mathematics 、 Gravitational singularity 、 Mathematical analysis 、 Conical surface 、 Surface (mathematics) 、 Riemann surface
摘要: We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two 9pi - theta, a suitable cos(theta) in Q(sqrt{19}). Relying on some delicate capacity estimates, we also show that the not conformally equivalent to hyperbolic maximal systole, yielding first example extremality this behavior.
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