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math.MG2025
Isoperimetric inequalities in Hadamard spaces of asymptotic rank two
Urs Lang, Stephan Stadler, David Urech
Gromov's isoperimetric gap conjecture for Hadamard spaces states that cycles in dimensions greater than or equal to the asymptotic rank admit linear isoperimetric filling inequalit…
math.MG2025
Minimal tetrahedra and an isoperimetric gap theorem in non-positive curvature
Cornelia Druţu, Urs Lang, Panos Papasoglu +1
We investigate isoperimetric inequalities for Lipschitz 2-spheres in CAT(0) spaces, proving bounds on the volume of efficient null-homotopies. In one dimension lower, it is known t…