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We prove optimal systolic inequalities on Finsler Mobius bands relating thesystole and the height of the Mobius band to its Holmes-Thompson volume. Wealso establish an optimal systolic in- equality for Finsler Klein bottles ofrevolution, which we conjecture to hold true for arbitrary Finsler metrics.Extremal metric families both on the Mobius band and the Klein bottle are alsopresented.

Optimal systolic inequalities on Finsler Mobius bands