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math.DG2025
Toponogov comparison and the collar theorem for complete surfaces with an appendix on the level sets of distance functions
Peter Buser, Jose M. Rodriguez
In the 1970s, the collar theorem was proven, establishing the existence of uniform tubular neighborhoods of simple closed geodesics on compact surfaces, whose widths depend only on…
math.DG2024
Translation surfaces with large systoles
Peter Buser, Eran Makover, Bjoern Muetzel
In this paper we continue to investigate the systolic landscape of translation surfaces started in [CHMW]. We show that there is an infinite sequence of surfaces of g…