64 research outputs found
Metric minimizing surfaces revisited
A surface which does not admit a length nonincreasing deformation is called
metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are
locally CAT(0) with respect to their intrinsic metric
Long geodesics on convex surfaces
We review the theory of intrinsic geometry of convex surfaces in the
Euclidean space and prove the following theorem: if the surface of a convex
body K contains arbitrary long closed simple geodesics, then K is an isosceles
tetrahedron.Comment: 8 pages, 10 figure
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