29 citations · 187 across the 52 of their papers we have counts for
4 papers · 2 filters
On intrinsic geometry of surfaces in normed spaces
Dmitri Burago, Sergei Ivanov
We prove three facts about intrinsic geometry of surfaces in a normed (Minkowski) space. When put together, these facts demonstrate a rather intriguing picture. We show that (1) ge…
Area minimizers and boundary rigidity of almost hyperbolic metrics
Dmitri Burago, Sergei Ivanov
This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are b…
On Gromov-Hausdorff stability in a boundary rigidity problem
Sergei Ivanov
Let be a compact Riemannian manifold with boundary. We show that is Gromov-Hausdorff close to a convex Euclidean region of the same dimension if the boundary distance f…
Volume comparison via boundary distances
Sergei Ivanov
The main subject of this expository paper is a connection between Gromov's filling volumes and a boundary rigidity problem of determining a Riemannian metric in a compact domain by…