Riemannian L Center of Mass: Existence, Uniqueness, and Convexity

  title={Riemannian L Center of Mass: Existence, Uniqueness, and Convexity},
  author={Bijan Afsari},
Let M be a complete Riemannian manifold and ν a probability measure on M . Assume 1 ≤ p ≤ ∞. We derive a new bound (in terms of p, the injectivity radius of M and an upper bound on the sectional curvatures of M) on the radius of a ball containing the support of ν which ensures existence and uniqueness of the global Riemannian Lp center of mass with respect to ν. A significant consequence of our result is that under the best available existence and uniqueness conditions for the so-called “local… CONTINUE READING
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