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Numerical Functional Analysis and Optimization Volume 35, 2014 - Issue 7-9: Variational Analysis and Applications
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Original Articles

A Notion of Nonlocal Curvature

Nicola Abatangelo Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, UMR CNRS 7352, Université de Picardie Jules Verne, Amiens, France; Dipartimento di Matematica Federigo Enriques, Università degli Studi di Milano, Milano, Italy
&
Enrico Valdinoci Dipartimento di Matematica Federigo Enriques, Università degli Studi di Milano, Milano, Italy; Weierstraß Institut für Angewandte Analysis und Stochastik, Berlin, GermanyCorrespondence[email protected]
Pages 793-815 | Received 08 Jan 2013, Accepted 06 Jun 2013, Published online: 08 Jul 2014

Citations (42)

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A. Cesaroni, L. De Luca, M. Novaga & M. Ponsiglione. (2021) Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows. Communications in Partial Differential Equations 46:7, pages 1344-1371.
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C. Mihaila. (2018) Axial symmetry for fractional capillarity droplets. Communications in Partial Differential Equations 43:12, pages 1673-1701.
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Articles from other publishers (40)

Alessandra De Luca, Serena Dipierro & Enrico Valdinoci. (2023) Nonlocal capillarity for anisotropic kernels. Mathematische Annalen 388:4, pages 3785-3846.
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Solveig Hepp & Moritz Kassmann. (2023) The divergence theorem and nonlocal counterparts. Bulletin of the London Mathematical Society 56:2, pages 711-733.
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Roberto Paroni, Paolo Podio-Guidugli & Brian Seguin. (2023) On a Notion of Nonlocal Curvature Tensor. Journal of Elasticity 154:1-4, pages 61-79.
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Anoumou Attiogbe, Mouhamed Moustapha Fall & Tobias Weth. (2023) Short time existence and smoothness of the nonlocal mean curvature flow of graphs. Mathematische Annalen.
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Michael Hinz & Jörn Kommer. (2023) A tensor product approach to non-local differential complexes. Mathematische Annalen.
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Lei Qin. (2023) Nonlocal energies of convex bodies and their log-Minkowski problems. Advances in Mathematics 427, pages 109132.
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Imad El BouchairiAbderrahim ElmoatazJalal Fadili. (2023) Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification. SIAM Journal on Imaging Sciences 16:1, pages 368-392.
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Daniele De Gennaro, Andrea Kubin & Anna Kubin. (2023) Asymptotic of the discrete volume-preserving fractional mean curvature flow via a nonlocal quantitative Alexandrov theorem. Nonlinear Analysis 228, pages 113200.
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Annalisa Cesaroni & Matteo Novaga. (2022) Fractional mean curvature flow of Lipschitz graphs. manuscripta mathematica 170:3-4, pages 427-451.
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Serena Dipierro, Fumihiko Onoue & Enrico Valdinoci. (2022) (Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property. Proceedings of the American Mathematical Society.
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L. De Luca, A. Kubin & M. Ponsiglione. (2022) The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows. Nonlinear Analysis 214, pages 112585.
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Matteo Cozzi & Luca Lombardini. (2021) On nonlocal minimal graphs. Calculus of Variations and Partial Differential Equations 60:4.
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Anoumou Attiogbe, Mouhamed Moustapha Fall & El Hadji Abdoulaye Thiam. (2021) Nonlocal diffusion of smooth sets. Mathematics in Engineering 4:2, pages 1-22.
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Annalisa Cesaroni & Valerio Pagliari. (2021) Convergence of nonlocal geometric flows to anisotropic mean curvature motion. Discrete & Continuous Dynamical Systems 41:10, pages 4987.
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Annalisa Cesaroni & Matteo Novaga. (2019) Symmetric Self-Shrinkers for the Fractional Mean Curvature Flow. The Journal of Geometric Analysis 30:4, pages 3698-3715.
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Eleonora Cinti, Carlo Sinestrari & Enrico Valdinoci. (2020) Convex sets evolving by volume-preserving fractional mean curvature flows. Analysis & PDE 13:7, pages 2149-2171.
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Claudia Bucur. (2020) A symmetry result in $${\mathbb {R}}^2$$ for global minimizers of a general type of nonlocal energy. Calculus of Variations and Partial Differential Equations 59:2.
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Ignace Aristide Minlend, Alassane Niang & El hadji Abdoulaye Thiam. (2020) Multiply-periodic hypersurfaces with constant nonlocal mean curvature. ESAIM: Control, Optimisation and Calculus of Variations 26, pages 10.
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Brian Seguin. (2019) A Fractional Notion of Length and an Associated Nonlocal Curvature. The Journal of Geometric Analysis 30:1, pages 161-181.
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Brian Seguin. (2019) A transport theorem for nonconvecting open sets on an embedded manifold. Continuum Mechanics and Thermodynamics 32:1, pages 1-8.
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José M. Mazón, Julio D. Rossi & Julián Toledo. (2019) Nonlocal perimeter, curvature and minimal surfaces for measurable sets. Journal d'Analyse Mathématique 138:1, pages 235-279.
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Enrico Valdinoci, Claudia Bucur & Luca Lombardini. (2019) Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36:3, pages 655-703.
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Serena Dipierro, Enrico Valdinoci & Vincenzo Vespri. (2019) Decay estimates for evolutionary equations with fractional time-diffusion. Journal of Evolution Equations 19:2, pages 435-462.
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Xavier Cabré & Matteo Cozzi. (2019) A gradient estimate for nonlocal minimal graphs. Duke Mathematical Journal 168:5.
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Vincent Millot, Yannick Sire & Kelei Wang. (2018) Asymptotics for the Fractional Allen–Cahn Equation and Stationary Nonlocal Minimal Surfaces. Archive for Rational Mechanics and Analysis 231:2, pages 1129-1216.
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José M. Mazón, Julio Daniel Rossi & J. Julián ToledoJosé M. Mazón, Julio Daniel Rossi & J. Julián Toledo. 2019. Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets. Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets 29 44 .
Xavier Cabré, Mouhamed Moustapha Fall, Joan Solà-Morales & Tobias Weth. (2018) Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay. Journal für die reine und angewandte Mathematik (Crelles Journal) 2018:745, pages 253-280.
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Mouhamed Moustapha Fall. (2018) Periodic patterns for a model involving short-range and long-range interactions. Nonlinear Analysis 175, pages 73-107.
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Giulio Ciraolo, Alessio Figalli, Francesco Maggi & Matteo Novaga. (2018) Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Journal für die reine und angewandte Mathematik (Crelles Journal) 2018:741, pages 275-294.
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Xavier Cabré, Mouhamed Moustapha Fall & Tobias Weth. (2017) Near-sphere lattices with constant nonlocal mean curvature. Mathematische Annalen 370:3-4, pages 1513-1569.
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Serena Dipierro & Enrico Valdinoci. (2018) (Non)local and (non)linear free boundary problems. Discrete & Continuous Dynamical Systems - S 11:3, pages 465-476.
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Brian Seguin, Paolo Podio-Guidugli & Roberto Paroni. (2017) On the nonlocal curvatures of surfaces with or without boundary. Communications on Pure and Applied Analysis 17:2, pages 709-727.
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Serena Dipierro, Aram Karakhanyan & Enrico Valdinoci. (2017) A class of unstable free boundary problems. Analysis & PDE 10:6, pages 1317-1359.
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Serena Dipierro, Aram Karakhanyan & Enrico Valdinoci. (2017) New Trends in Free Boundary Problems. Advanced Nonlinear Studies 17:2, pages 319-332.
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Annalisa Cesaroni & Matteo Novaga. (2017) Volume constrained minimizers of the fractional perimeter with a potential energy. Discrete and Continuous Dynamical Systems - Series S 10:4, pages 715-727.
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Serena Dipierro, Matteo Novaga & Enrico Valdinoci. (2017) Rigidity of critical points for a nonlocal Ohta–Kawasaki energy. Nonlinearity 30:4, pages 1523-1535.
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Juan Dávila, Manuel del Pino, Serena Dipierro & Enrico Valdinoci. (2016) Nonlocal Delaunay surfaces. Nonlinear Analysis 137, pages 357-380.
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Claudia Bucur & Enrico ValdinociClaudia Bucur & Enrico Valdinoci. 2016. Nonlocal Diffusion and Applications. Nonlocal Diffusion and Applications 97 126 .
Eleonora Cinti & Fausto Ferrari. (2015) Geometric inequalities for fractional Laplace operators and applications. Nonlinear Differential Equations and Applications NoDEA 22:6, pages 1699-1714.
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Matteo Cozzi. (2015) On the variation of the fractional mean curvature under the effect of $C^{1, \alpha}$ perturbations. Discrete and Continuous Dynamical Systems 35:12, pages 5769-5786.
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