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Creators/Authors contains: "Berdnikov, Aleksandr"

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  1. ; ; (, Forum of Mathematics, Pi)
    Abstract We study the degree of an L-Lipschitz map between Riemannian manifolds, proving new upper bounds and constructing new examples. For instance, if $$X_k$$ is the connected sum of k copies of $$\mathbb CP^2$$for$$k \ge 4$$, then we prove that the maximum degree of an L-Lipschitz self-map of $$X_k$$ is between $$C_1 L^4 (\log L)^{-4}$$ and $$C_2 L^4 (\log L)^{-1/2}$$. More generally, we divide simply connected manifolds into three topological types with three different behaviors. Each type is defined by purely topological criteria. For scalable simply connected n-manifolds, the maximal degree is $$\sim L^n$$. For formal but nonscalable simply connectedn-manifolds, the maximal degree grows roughly like $$L^n (\log L)^{-\theta (1)}$$. And for nonformal simply connected n-manifolds, the maximal degree is bounded by $$L^\alpha $$ for some $$\alpha < n$$. 
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  2. ; (, Inventiones mathematicae)
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