Glen Wheeler

The Cartan-Hadamard isoperimetric inequality under controlled variation of curvature

We prove the Cartan-Hadamard conjecture (the sharp Euclidean isoperimetric inequality) in every dimension, assuming that the sectional curvature is pinched relative to a reference radius of curvature. The reference radius of curvature may vary, and the condition includes examples where the radius of curvature blows up,...