Harmonic Analysis
Philipp Reiter

Publications

Refereed articles

  • Simon Blatt, Philipp Reiter, Armin Schikorra, and Nicole Vorderobermeier. Scale-invariant tangent-point energies for knots. Accepted for publication by Journal of the European Mathematical Society, 2024. [ arXiv ]
  • Stefan Krömer and Philipp Reiter. Nonlinear elasticity with vanishing nonlocal self-repulsion. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2023. [ arXiv | doi ]
  • Simon Blatt, Philipp Reiter, and Armin Schikorra. On O'hara knot energies I: Regularity for critical knots. J. Differential Geom. 121(3):385–424, 2022. [ arXiv | doi ]
  • Alexandra Gilsbach, Philipp Reiter, and Heiko von der Mosel. Symmetric elastic knots. Math. Ann., 385:811–844, 2023. [ arXiv | doi ]
  • Yuanan Diao, Claus Ernst, and Philipp Reiter. Knots with equal bridge index and braid index. J. Knot Theory Ramifications, 30(11):2150075, 2021. [ arXiv | doi ]
  • Philipp Reiter and Henrik Schumacher. Sobolev Gradients for the Möbius Energy. Arch. Rat. Mech. Anal., 242:701–746, 2021. [ arXiv | doi ]
  • Sören Bartels and Philipp Reiter. Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves. Math. Comp., 90:1499–1526, 2021. [ arXiv | doi ]
  • Sören Bartels and Philipp Reiter. Numerical solution of a bending-torsion model for elastic rods. Numer. Math., 146:661–697, 2020. [ arXiv | doi ]
  • Jason Cantarella, Kyle Chapman, Philipp Reiter, and Clayton Shonkwiler. Open and closed random walks with fixed edgelengths in \(\mathbb R^d\). Journal of Physics A: Mathematical and Theoretical, 51(43):434002, 2018. [ arXiv | doi ]
  • Sören Bartels, Philipp Reiter, and Johannes Riege. A simple scheme for the approximation of self-avoiding inextensible curves. IMA J. Numer. Anal., 38(2):543–565, 2018. [ preprint | doi ]
  • Henryk Gerlach, Philipp Reiter, and Heiko von der Mosel. The elastic trefoil is the doubly covered circle. Arch. Rat. Mech. Anal., 225(1):89–139, 2017. [ arXiv | doi ]
  • Paola Pozzi and Philipp Reiter. On non-convex anisotropic surface energy regularized via the Willmore functional: the two-dimensional graph setting. ESAIM: COCV, 23(3):1047–1071, 2017. [ preprint | doi ]
  • Simon Blatt, Philipp Reiter, and Armin Schikorra. Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth. Trans. Amer. Math. Soc., 368:6391–6438, 2016. [ arXiv | doi ]
  • Simon Blatt and Philipp Reiter. Towards a regularity theory for integral Menger curvature. Ann. Acad. Sci. Fenn. Math., 40(1):149–181, 2015. [ arXiv | doi ]
  • Simon Blatt and Philipp Reiter. Regularity theory for tangent-point energies: The non-degenerate sub-critical case. Adv. Calc. Var., 8(2):93–116, 2015. [ arXiv | doi ]
  • Simon Blatt and Philipp Reiter. Modeling repulsive forces on fibres via knot energies. Mol. Based Math. Biol., 2(1):56–72, 2014. [ preprint | doi ]
  • Paola Pozzi and Philipp Reiter. Willmore-type regularization of mean curvature flow in the presence of a non-convex anisotropy. The graph setting: analysis of the stationary case and numerics for the evolution problem. Advances in Differential Equations, 18(3–4):265–308, 2013. [ preprint | link ]
  • Simon Blatt and Philipp Reiter. Stationary points of O’Hara’s knot energies. Manuscripta Math., 40(1-2):29–50, 2013. [ arXiv | doi ]
  • Philipp Reiter. Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family \(E^{(\alpha)}\), \(\alpha\in[2,3)\). Math. Nachr., 285(7):889–913, 2012. [ preprint | doi ]
  • Philipp Reiter. Regularity theory for the Möbius energy. Commun. Pure Appl. Anal., 9(5):1463–1471, 2010. [ preprint | doi ]
  • Wolfgang Alt, Dieter Felix, Philipp Reiter, and Heiko von der Mosel. Energetics and dynamics of global integrals modeling interaction between stiff filaments. J. Math. Biol., 59(3):377–414, 2009. [ preprint | doi ]
  • Simon Blatt and Philipp Reiter. Does finite knot energy lead to differentiability? J. Knot Theory Ramifications, 17(10):1281–1310, 2008. [ preprint | doi ]

Edited book

  • Simon Blatt, Philipp Reiter, and Armin Schikorra, editors. New directions in Geometric and Applied Knot Theory. De Gruyter, 2018. [ doi ]

Proceedings

  • Simon Blatt, Philipp Reiter, and Armin Schikorra. Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings. Oberwolfach Rep., 17(4):1823–1856, 2020. [ doi ]
  • Simon Blatt and Philipp Reiter. How nice are critical knots? Regularity theory for knot energies. J. Phys.: Conf. Ser. 544 012020, 2014. [ doi ]
  • Paola Pozzi and Philipp Reiter. Approximation of non-convex anisotropic energies via Willmore energy, CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna. [ preprint | link ]