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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Concentration properties of inner-products in high-dimension
Let $S^K$ be the unit sphere embedded in $R^{K+1}$.
$v \in S^K$ is randomly chosen from a uniform distribution over $S^K$.
$A \subseteq S^K$ is a $d$-dimensional sub-manifold ($d \leq K$). Think of …