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Results tagged with riemannian-geometry
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user 9791
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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Are packing-homogeneous spaces homogeneous?
Given a metric space (M,d) define the packing function P(x,R,r) to be the maximum number of non-intersecting balls of radius r with centers in the ball B(x,R). Let’s call M packing-homogeneous if the …
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Closed geodesics on bumpy spheres
For any Riemannian metric on the 2-sphere there exist 3 simple closed geodesics of length at most 20d, where d is the diameter of the 2-sphere. This result is proved here: https://arxiv.org/pdf/1410.8 …