Veröffentlichungen
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Elastic BB knots are multifold circles
arXiv:2609.22575 [math.DG]
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Stability of knot equivalence at low regularity, and symmetric critical knots for the Möbius energy
arXiv:2512.02998 [math.GT]
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On the Palais-Smale condition in geometric knot theory
arXiv:2505.02719 [math.CA]
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Optimal planar immersions of prescribed winding number and Arnold invariants
Nonlinear Analysis TMA 263 (2026) 113942.
doi:10.1016/j.na.2025.113942, arXiv:2407.04032 [math.CA]
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Banach gradient flows for various families of knot energies
J. Evol. Equations 23, 31 (2023).
doi:10.1007/s00028-022-00863-x, arXiv:2204.13603 [math.CA]
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Tangent-point energies and ropelength as Gamma-limit of discrete tangent-point energies on biarc curves
Advances in Continuous and Discrete Models: Theory and Applications (2023) 2023:4.
doi:10.1186/s13662-022-03750-4, arXiv:2203.16383 [math.CA]
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Symmetric elastic knots
Math. Ann. online Feb. 2022.
doi:10.1007/s00208-021-02346-9, arXiv:2105.08558 [math.DG]
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A speed preserving Hilbert gradient flow for generalized integral Menger curvature
Adv. Calc. Var. 16(3) (2023), 597--635.
doi:https://doi.org/10.1515/acv-2021-0037, arXiv:2103.10408 [math.CA]
Vgl. auch:
Zweitveröffentlichung (Open Access)
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Möbius-invariant self-avoidance energies for non-smooth sets of arbitrary dimensions and co-dimension
Advances in Mathematics 426 (2023) 109108
doi:https://doi.org/10.1016/j.aim.2023.109108, arXiv:2010.03906v2 [math.DG]
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Möbius-invariant self-avoidance energies for non-smooth sets in arbitrary dimensions
Oberwolfach Mini-Workshop Nonlocal Analysis and the Geometry of Embeddings (hybrid meeting Nov. 2020); abstract available in: Oberwolfach Report No. 37/2020
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Geometric curvature energies: facts, trends, and open problems
In: New Directions in Geometric and Applied Knot Theory (ed. P. Reiter, S. Blatt, A. Schikorra), De Gruyter 2018, pp. 8--35.
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Singular support of minimizers of the causal variational principle on the sphere
Calc. Var. (2019) 58:205.
doi:10.1007/s00526-019-1652-7, arXiv:1808.09754v3 [math.CA]
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Symmetric critical knots for O'Hara's energies
Topology and its Applications 242 (2018), 73--102.
doi:10.1016/j.topol.2018.04.014, arXiv:1709.06949v2 [math.CA] PDF
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The Plateau problem for the Busemann-Hausdorff area in arbitrary codimension
European J. Math. Vol. 3, Issue 4 (2017), 953--973.
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The elastic trefoil is the doubly covered circle
Arch. Rational Mech. Anal. 225 (2017), 89--139.
doi:10.1007/s00205-017-1100-9, arXiv:1510.06171v1 [math.DG] PDF
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Compactness and isotopy finiteness for submanifolds with uniformly bounded geometric curvature energies
Communications in Analysis and Geometry 26 (2019), 1251--1316.
doi:10.4310/CAG.2018.v26.n6.a2, arXiv:1504.04538v1 [math.DG] PDF
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Xavier Tolsa: “Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón-Zygmund Theory”
Jahresber. DMV Vol. 117, Issue 3 (2015), 217--223.
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On minimal immersions in Finsler space
Annals of Global Analysis and Geometry Vol. 48, Issue 4 (2015), 397--422.
doi:10.1007/s10455-015-9476-y, arXiv:1403.8025v1 [math.DG] PDF
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How averaged Menger curvatures control regularity and topology of curves and surfaces.
Journal of Physics: Conference Series 544 (2014) 012018
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Menger curvature as a knot energy.
Physics Reports 530 (2013), 257--290
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Plateau's problem in Finsler 3-space.
Manuscripta Mathematica 143 (2014), 273--316
doi:10.1007/s00229-013-0626-x, arXiv:1209.2327v1 [math.DG] PDF
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On some knot energies involving Menger curvature.
Topology and its Applications 160 (2013), 1507--1529
doi:10.1016/j.topol.2013.05.022, arXiv:1209.1527v1 [math.CA] PDF
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Characterizing W2,p submanifolds by p-integrability of global curvatures.
Geometric Functional Analysis 23, no. 3 (2013), 937--984
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Tangent-point repulsive potentials for a class of non-smooth m-dimensional sets in Rn. Part I: Smoothing and self-avoidance effects.
J. Geometric Analysis 23, no. 3 (2013), 1085--1139
doi:10.1007/s12220-011-9275-z, arXiv:1102.3642v1 [math.CA] PDF
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Tangent-point self-avoidance energies for curves.
J. Knot Theory Ramifications 21, no. 5 (2012)
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On sphere-filling ropes.
Amer. Math. Monthly 118, no. 10 (2011), 863--876
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Integral Menger curvature for surfaces.
Adv. Math. 226 (2011), 2233--2304
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What are the longest ropes on the unit sphere?
Arch. Rational Mech. Anal. 201 (2011), 303--342
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Regularizing and self-avoidance effects of integral Menger curvature.
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010), 145--187 PDF
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Yin-Yang-Kurven lösen ein Packungsproblem (Yin-Yang curves solve a packing problem).
RWTH-Themen 2/2008, Wissenschaftsmagazin RWTH Aachen University (2008), 26--29 PDF
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Conformal mapping of multiply connected Riemann domains by a variational approach.
Adv. Calc. Var. 2 (2009), 137--183
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Energetics and dynamcis of global integrals modeling interaction between stiff filaments.
J. Mathematical Biology 59 (2009), 377--414
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A geometric curvature double integral of Menger type for space curves.
Ann. Acad. Scient. Fenn. Math. 34 (2009), 195--214 PDF
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Obstacle problems for elastic rods.
Preprint Nr. 16 Institut f. Mathematik, RWTH Aachen University (2007) PDF
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On weakly harmonic maps from Finsler to Riemannian manifolds.
Annales de l'I.H.P. -- Analyse non lineaire 26 (2009), 39--57
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On rectifiable curves with Lp bounds on global curvature: Self-avoidance, regularity, and minimizing knots.
Math. Z. 257 (2007), 107--130
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Conformal representation of surfaces, and Plateau's problem for Cartan functionals.
Rivista di Matematica della Univ. di Parma, Ser. 7, vol. 4* (2005), 1--43 PDF
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Global curvature for surfaces and area minimization under a thickness constraint.
Calc. Var. 25 (2006), 431--467
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On Lichtenstein's theorem about globally conformal mappings.
Calc. Var. 23 (2005), 415--424
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On a mathematical model for thick surfaces.
In: Calvo, Millett, Rawdon, Stasiak (eds.) Physical and Numerical Models in Knot Theory. Ser. on Knots and Everything 36, World Scientific 2005, 547--564
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Plateau's problem for parametric double integrals. Part II: Regularity at the boundary.
J. reine angew. Math. 565 (2003), 207--233
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On surfaces of prescribed F-mean curvature.
Pac. J. Math. 213 (2004), 15--36
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The Douglas problem for parametric double integrals.
manunscripta math. 110 (2003), 93--114
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Euler-Lagrange equations for nonlinearly elastic rods with self-contact.
Arch. Rational Mech. Anal. 168 (2003), 35--82
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Dominance functions for parametric Lagrangians.
In: Geometric analysis and nonlinear partial differential equations, Springer Berlin Heidelberg New York 2002, 297--326 DVI
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The partially free boundary problem for parametric double integrals.
In: Nonlinear Problems in Mathematical Physics and Related Topics I, in honor of Prof. O.A. Ladyzhenskaya, T. Rozhkovskaya, K. Derham (eds.),
Scientific Books Publ. (Russian), Kluwer (Engl.) 2002, 145--165
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Plateau's problem for parametric double integrals. Part I: Existence and regularity in the interior.
Comm. Pure Appl. Math. 56 (2003), 926-955
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Existence and Regularity for Nonlinear Elastic Self-Contact Problems.
Habilitation thesis, Universität Bonn, 2001, Bonner Mathematische Schriften 349, 2002
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Isoperimetric inequalities for parametric variational problems.
Ann. de l'I.H.P. -- Analyse non lineaire 19 (2002), 617--629
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Global curvature and self-contact of nonlinearly elastic curves and rods.
Calc. Var. 14 (2002), 29--68
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Ordinary Differential Equations with Measurable Right-Hand Side and Parameters in Metric Spaces.
Preprint 676, SFB 256, Uni-Bonn (2000) DVI
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Compactness Theorems and an Isoperimetric Inequality for Critical Points of Elliptic Parametric Functionals.
Calc. Var 12 (2001), 85--107
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On two-dimensional parametric variational problems.
Calc. Var. 9 (1999), 249--267
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Elastic knots in Euclidean 3-space
Ann. de l'I.H.P. -- Analyse non lineaire 16 no.2 (1999), 137--166
doi:10.1016/S0294-1449(99)80010-9
Vgl. auch:
Addendum to publications 2, 4 and 5 (by P. Reiter, 2004)
,
Updated addendum (by P. Reiter, 2005).
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Minimizing the elastic energy of knots.
Asymptotic Analysis 18 (1998), 49--65
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Nonexistence Results for Extremals of Curvature Functionals.
Archiv d. Math. 69 (1997), 427--434
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Geometrische Variationsprobleme höherer Ordnung.
Dissertation, Universität Bonn 1996,Bonner Mathematische Schriften 293, 1996
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Regularität von Lösungen parametrischer Variationsprobleme.
Diploma thesis, Universität Bonn 1992