منابع مشابه
Nearly round spheres look convex
We prove that a Riemannian manifold (M, g), close enough to the round sphere in the C topology, has uniformly convex injectivity domains — so M appears uniformly convex in any exponential chart. The proof is based on the Ma–Trudinger–Wang nonlocal curvature tensor, which originates from the regularity theory of optimal transport.
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In this paper the regularity of optimal transportation potentials dened on round spheres is investigated. Speci cally, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satis ed on the round sphere, when the cost-function is the geodesic distance squared. In order to generalise Loeper's calculation to a broader cla...
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A closed Riemannian manifold M is said to have cross (compact rank one symmetric space) blocking if whenever p 6= q are less than the diameter apart, all light rays from p can be shaded away from q with at most two point shades. Similarly, a closed Riemannian manifold is said to have sphere blocking if for each p ∈M all the light rays from p are shaded away from p by a single point shade. We pr...
متن کاملAn Almost-Constant Round Interactive Zero-Knowledge Proof
The concept of interactive zero-knowledge proofs (IZKPs) was introduced by Goldwasser, Micali and Rackoff [13]. They considered a setting in which a “powerful” prover P wants to convince a verifier V that a string x belongs to a language L c (0, l}*. With interactive proofs, P and I/ may toss coins and exchange messages (strings). Thus when x EL, V is only convinced with a high probability, gre...
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It is known that perfectly secure (1-round, n-channel) message transmission (MT) schemes exist if and only if n ≥ 3t + 1, where t is the number of channels that the adversary can corrupt. Then does there exist an almost secure MT scheme for n = 2t + 1 ? In this paper, we first sum up a number flaws of the previous almost secure MT scheme presented at Crypto 2004 . We next show an equivalence be...
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ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 1994
ISSN: 1340-6116
DOI: 10.2206/kyushujm.48.169