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math.DG2004
Boundary case of equality in optimal Loewner-type inequalities
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
We prove certain optimal systolic inequalities for a closed Riemannian manifold (X,g), depending on a pair of parameters, n and b. Here n is the dimension of X, while b is its firs…
math.DG2004
Generalized degree and optimal Loewner-type inequalities
Sergei V. Ivanov, Mikhail G. Katz
We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool…
math.DG2004
Filling area conjecture and ovalless real hyperelliptic surfaces
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus…