In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 267-280
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In: Annals of Global Analysis and Geometry, 2015, vol. 47, no. 3, p. 285-304
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In: Manuscripta Mathematica, 2015, vol. 147, no. 3-4, p. 365-380
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In: Communications in Mathematical Physics, 2015, vol. 338, no. 3, p. 1327-1361
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In: Advances in Calculus of Variations, 2017, vol. 10, no. 4, p. 407-421
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In: Discrete Applied Mathematics, 2020, vol. 276, p. 115–120
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In: Geometriae Dedicata, 2020, p. -
This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi- isometric classification with the bi-Lipschitz classification. On the...
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In: Mathematische Annalen, 2019, vol. 373, no. 3, p. 1177–1210
We prove that any proper, geodesic metric space whose Dehn function grows asymptotically like the Euclidean one has asymptotic cones which are non-positively curved in the sense of Alexandrov, thus are CAT(0) . This is new already in the setting of Riemannian manifolds and establishes in particular the borderline case of a result about the sharp isoperimetric constant which implies Gromov...
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In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2015, vol. 2015, no. 705, p. 233-244
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In: Annali di Matematica Pura ed Applicata (1923 -), 2019, vol. 198, no. 2, p. 367–380
We prove local Hölder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Hölder continuity of such mappings from bounded Lipschitz domains.
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