For each fixed real 1 < p < infinity with p != 2 and distortion D > 1, every n-point subset of a real Lp space has a nonlinear embedding into finite-dimensional l_p with dimension at most exp(C(p,D) (log n)^gamma), where gamma = 2-p for p < 2 and 1-2/p for p > 2.
For each fixed real 1 < p < infinity with p != 2 and distortion D > 1, every n-point subset of a real Lp space has a nonlinear embedding into finite-dimensional l_p with dimension at most exp(C(p,D) (log n)^gamma), where gamma = 2-p for p < 2 and 1-2/p for p > 2.
For each fixed real 1 < p < infinity with p != 2 and distortion D > 1, every n-point subset of a real Lp space has a nonlinear embedding into finite-dimensional l_p with dimension at most exp(C(p,D) (log n)^gamma), where gamma = 2-p for p < 2 and 1-2/p for p > 2.
If correct, replaces linear dependence on the number of points by subpolynomial dimension for nonlinear finite-set embeddings in every fixed real Lp space with 1 < p < infinity.
Can every finite subset of real Lp, for 1 < p < infinity, be embedded in subpolynomial dimension at any fixed distortion greater than one?
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