Tangent-point energies and ropelength as Gamma-limits of discrete tangent-point energies on biarc curves

[1]  H. von der Mosel,et al.  Banach gradient flows for various families of knot energies , 2022, Journal of Evolution Equations.

[2]  Alexander R. Klotz,et al.  The ropelength of complex knots , 2021, Journal of Physics A: Mathematical and Theoretical.

[3]  Keenan Crane,et al.  Repulsive surfaces , 2021, ACM Trans. Graph..

[4]  Henrik Schumacher,et al.  A speed preserving Hilbert gradient flow for generalized integral Menger curvature , 2021, Advances in Calculus of Variations.

[5]  Keenan Crane,et al.  Repulsive Curves , 2020, ACM Trans. Graph..

[6]  Max Wardetzky,et al.  Variational convergence of discrete elasticae , 2019, IMA Journal of Numerical Analysis.

[7]  Sören Bartels,et al.  A simple scheme for the approximation of self-avoiding inextensible curves , 2018 .

[8]  Soren Bartels,et al.  Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves , 2018, Math. Comput..

[9]  Sebastian Scholtes.  Discrete knot energies , 2016, 1603.02464.

[10]  S. Blatt.  Curves Between Lipschitz and $$C^1$$C1 and Their Relation to Geometric Knot Theory , 2016, The Journal of Geometric Analysis.

[11]  Sebastian Scholtes.  Discrete thickness , 2014, 1401.5651.

[12]  Sebastian Scholtes.  Discrete M\"obius Energy , 2013, 1311.3056.

[13]  Simon Blatt,et al.  THE ENERGY SPACES OF THE TANGENT POINT ENERGIES , 2013 .

[14]  H. Mosel,et al.  On some knot energies involving Menger curvature , 2012, 1209.1527.

[15]  Simon Blatt,et al.  Regularity theory for tangent-point energies: The non-degenerate sub-critical case , 2012, 1208.3605.

[16]  Jason H. Cantarella,et al.  Shapes of tight composite knots , 2011, 1110.3262.

[17]  Heiko von der Mosel,et al.  Tangent-point self-avoidance energies for curves , 2010, 1006.4566.

[18]  Eric J. Rawdon,et al.  Knot Tightening by Constrained Gradient Descent , 2010, Exp. Math..

[19]  John H. Maddocks,et al.  BIARCS, GLOBAL RADIUS OF CURVATURE, AND THE COMPUTATION OF IDEAL KNOT SHAPES , 2005 .

[20]  J. Simon,et al.  POLYGONAL APPROXIMATION AND ENERGY OF SMOOTH KNOTS , 2003, math/0305414.

[21]  Andrea Braides.  Gamma-Convergence for Beginners , 2002 .

[22]  Jason H. Cantarella,et al.  On the minimum ropelength of knots and links , 2001, math/0103224.

[23]  J. Maddocks,et al.  Global curvature, thickness, and the ideal shapes of knots. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Karl-Theodor Sturm,et al.  New Directions in Dirichlet Forms , 1998 .

[25]  H. Alt,et al.  Linear Functional Analysis , 2016 .

[26]  Enrico Valdinoci,et al.  DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES , 2015 .

[27]  P. Reiter.  All curves in a C 1 -neighbourhood of a given embedded curve are isotopic , 2005 .

[28]  J. Smutny.  Global radii of curvature, and the biarc approximation of space curves , 2004 .

[29]  F. Schuricht,et al.  Global curvature for rectifiable loops , 2003 .

[30]  Julian Havil.  Gamma: Exploring Euler's Constant , 2003 .

[31]  Oscar Gonzalez,et al.  Curves, circles, and spheres , 2002 .

[32]  Andrea Braides.  Γ-convergence for beginners , 2002 .

[33]  G. D. Maso,et al.  An Introduction to-convergence , 1993 .

[34]  Jun O'Hara,et al.  Energy of a knot , 1991 .

[35]  O. Forster.  Differential- und Integralrechnung einer Veränderlichen , 1980 .

[36]  H. Piaggio.  Calculus of Variations , 1954, Nature.

[37]  O. Gonzalez,et al.  F Ur Mathematik in Den Naturwissenschaften Leipzig Global Curvature and Self-contact of Nonlinearly Elastic Curves and Rods Global Curvature and Self-contact of Nonlinearly Elastic Curves and Rods , 2022 .