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Creators/Authors contains: "Guth, Larry"

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  1. ; ; (, Journal of Topology and Analysis)
    We show that a complete [Formula: see text]-dimensional Riemannian manifold [Formula: see text] with finitely generated first homology has macroscopic dimension [Formula: see text] if it satisfies the following “macroscopic curvature” assumptions: every ball of radius [Formula: see text] in [Formula: see text] has volume at most [Formula: see text], and every loop in every ball of radius [Formula: see text] in [Formula: see text] is null-homologous in the concentric ball of radius [Formula: see text]. 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; ; (, Journal of the European Mathematical Society)
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  3. ; ; (, 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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  4. ; ; (, Journal of European Mathematical Society)
    We prove an l^2L^6 decoupling inequality for the parabola with constant .logR/c. In the appendix, we present an application to the sixth-order correlation of the integer solutions to x^2 +y^2 = m. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, Selecta Mathematica)
    null (Ed.)
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  6. ; ; (, Geometric and Functional Analysis)
    null (Ed.)
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  7. ; ; ; ; ; (, American Journal of Mathematics)
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  8. ; ; ; (, Inventiones mathematicae)
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  9. ; ; ; (, Forum of Mathematics, Sigma)
    We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $$n\geqslant 3$$ , $$\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$$ $=f(x)$ almost everywhere with respect to Lebesgue measure for all $$f\in H^{s}(\mathbb{R}^{n})$$ provided that $s>(n+1)/2(n+2)$ . The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya. 
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