Sobolev Gradients for the Möbius Energy

• Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves

  2024 Journal of Geometric Analysis article Mathematics Geometric Analysis and Curvature Flows Open access

  3

  citations
• From Knot Invariants to Knot Dynamics

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  0

  citations
• Möbius-invariant self-avoidance energies for non-smooth sets of arbitrary dimension and co-dimension

  2023 Advances in Mathematics article Mathematics Geometric Analysis and Curvature Flows

  1

  citations
• Banach gradient flows for various families of knot energies

  2023 Journal of Evolution Equations article Mathematics Geometric Analysis and Curvature Flows Open access

  3

  citations
• Computing confined elasticae

  2022 Advances in Continuous and Discrete Models article Engineering Advanced Numerical Analysis Techniques Open access

  0

  citations
• A speed preserving Hilbert gradient flow for generalized integral Menger curvature

  2022 Advances in Calculus of Variations article Mathematics Geometric Analysis and Curvature Flows Open access

  4

  citations
• M{ö}bius-invariant self-avoidance energies for non-smooth sets in arbitrary dimensions

  2020 arXiv (Cornell University) preprint Mathematics Nonlinear Partial Differential Equations Open access

  0

  citations

7 results

• Numerical optimization

  2021 Cambridge University Press eBooks book-chapter Computer Science Data Analysis with R

  14,036

  citations
• Interpolation Theory, Function Spaces, Differential Operators

  1978 North-Holland mathematical library book Mathematics Advanced Banach Space Theory

  4,428

  citations
• Theory of Function Spaces

  1983 Springer eBooks book Mathematics Mathematical and Theoretical Analysis

  4,325

  citations
• Hitchhikerʼs guide to the fractional Sobolev spaces

  2011 Bulletin des Sciences Mathématiques article Mathematics Nonlinear Partial Differential Equations Open access

  4,322

  citations
• A method for solving the convex programming problem with convergence rate O(1/k^2)

  1983 Medical Entomology and Zoology article Computer Science Optimization and Variational Analysis

  1,770

  citations
• Computing Discrete Minimal Surfaces and Their Conjugates

  1993 Experimental Mathematics article Mathematics Geometric Analysis and Curvature Flows

  1,278

  citations
• Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

  1996 De Gruyter eBooks book Mathematics Nonlinear Partial Differential Equations

  1,129

  citations
• Numerical Optimization (Springer Series in Operations Research and Financial Engineering)

  2000 book Mathematics Iterative Methods for Nonlinear Equations

  1,112

  citations
• Partial Differential Equations I: Basic Theory

  1996 CERN Document Server (European Organization for Nuclear Research) article Mathematics Differential Equations and Boundary Problems

  709

  citations
• Adaptive Restart for Accelerated Gradient Schemes

  2013 Foundations of Computational Mathematics article Computer Science Stochastic Gradient Optimization Techniques Open access

  667

  citations
• Ten Equivalent Definitions of the Fractional Laplace Operator

  2017 Fractional Calculus and Applied Analysis article Mathematics Differential Equations and Boundary Problems Open access

  619

  citations
• Discrete elastic rods

  2008 ACM Transactions on Graphics article Engineering Dynamics and Control of Mechanical Systems

  558

  citations
• Riemannian geometries on spaces of plane curves

  2006 Journal of the European Mathematical Society article Mathematics Geometric Analysis and Curvature Flows Open access

  386

  citations
• A Trust Region Algorithm for Nonlinearly Constrained Optimization

  1987 SIAM Journal on Numerical Analysis article Mathematics Advanced Optimization Algorithms Research

  362

  citations
• Partial Differential Equations I

  2010 Applied mathematical sciences book Mathematics Differential Equations and Boundary Problems

  352

  citations
• Fast Continuous Collision Detection between Rigid Bodies

  2002 Computer Graphics Forum article Computer Science Robotic Path Planning Algorithms Open access

  258

  citations
• Global curvature, thickness, and the ideal shapes of knots

  1999 Proceedings of the National Academy of Sciences article Mathematics Geometric and Algebraic Topology Open access

  257

  citations
• Mobius Energy of Knots and Unknots

  1994 Annals of Mathematics article Mathematics Geometric Analysis and Curvature Flows

  235

  citations
• A Proof of the Smale Conjecture, Diff(S 3 ) ≃O(4)

  1983 Annals of Mathematics article Mathematics Geometric and Algebraic Topology

  235

  citations
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach

  2007 Applied and Computational Harmonic Analysis article Mathematics Geometric Analysis and Curvature Flows Open access

  228

  citations