67 citations · 818 across the 113 of their papers we have counts for
45 papers · 1 filter
Extending Gromov's optimal systolic inequality
Thomas G. Goodwillie, James J. Hebda, Mikhail G. Katz
The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal…
New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below
Semyon Alesker, Mikhail Katz, Roman Prosanov
Let be a sequence of compact -dimensional Alexandrov spaces (e.g. Riemannian manifolds) with curvature uniformly bounded below which converges in the Gromov-Hausdorff…
Sharp reverse isoperimetric inequalities in nonpositively curved cones
Mikhail G. Katz, Stephane Sabourau
We prove a pair of sharp reverse isoperimetric inequalities for domains in nonpositively curved surfaces: (1) metric disks centered at the vertex of a Euclidean cone of angle at le…
A systolic inequality with remainder in the real projective plane
Mikhail G. Katz, Tahl Nowik
The first paper in systolic geometry was published by Loewner's student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary…
Metric completions, the Heine-Borel property, and approachability
Vladimir Kanovei, Mikhail G. Katz, Tahl Nowik
We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space. As mentioned…
Torus cannot collapse to a segment
Mikhail G. Katz
In earlier work, we analyzed the impossibility of codimension-one collapse for surfaces of negative Euler characteristic under the condition of a lower bound for the Gaussian curva…