List of publications

Preprints

Blatt S (2016), "The Gradient Flow of O'Hara's Knot Energies", January, 2016.
Abstract: Jun O'Hara invented a family of knot energies $E^j,p$, $j,p in (0, $. We study the negative gradient flow of the sum of one of the energies $E^alpha = E^1$, $alpha in (2,3)$, and a positive multiple of the length. Showing that the gradients of these knot energies can be written as the normal part of a quasilinear operator, we derive short time existence results for these flows. We then prove long time existence and convergence to critical points.
BibTeX:
@article{Blatt2016,
  author = {Simon Blatt},
  title = {The Gradient Flow of O'Hara's Knot Energies},
  year = {2016},
  url = {http://arxiv.org/abs/1601.02840}
}
Blatt S (2016), "The Gradient Flow of the Möbius energy: \(\varepsilon\)-regularity and consequences", January, 2016.
Abstract: In this article we study the gradient flow of the Möbius energy introduced by O'Hara in 1991. We will show a fundamental $\varepsilon$-regularity result that allows us to bound the infinity norm of all derivatives for some time if the energy is small on a certain scale. This result enables us to characterize the formation of a singularity in terms of concentrations of energy and allows us to construct a blow-up profile at a possible singularity. This solves one of the open problems listed by Zheng-Xu He. Ruling out blow-ups for planar curves, we will prove that the flow transforms every planar curve into a round circle.
BibTeX:
@article{Blatt2016a,
  author = {Simon Blatt},
  title = {The Gradient Flow of the Möbius energy: $\varepsilon$-regularity and consequences},
  year = {2016},
  url = {http://arxiv.org/abs/1601.07023}
}

Peer reviewed articles

Blatt S, Reiter P and Schikorra A (2016), "Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth", Trans. Amer. Math. Soc.. Vol. 368(9), pp. 6391-6438.
BibTeX:
@article{Blatt2016,
  author = {Blatt, Simon and Reiter, Philipp and Schikorra, Armin},
  title = {Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth},
  journal = {Trans. Amer. Math. Soc.},
  year = {2016},
  volume = {368},
  number = {9},
  pages = {6391--6438},
  url = {http://dx.doi.org/10.1090/tran/6603},
  doi = {10.1090/tran/6603}
}
Blatt S and Struwe M (2015), "Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow", Calc. Var. Partial Differential Equations. Vol. 54(2), pp. 2285.
BibTeX:
@article{Blatt2015,
  author = {Blatt, Simon and Struwe, Michael},
  title = {Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow},
  journal = {Calc. Var. Partial Differential Equations},
  year = {2015},
  volume = {54},
  number = {2},
  pages = {2285},
  url = {http://dx.doi.org/10.1007/s00526-015-0901-7},
  doi = {10.1007/s00526-015-0901-7}
}
Blatt S and Struwe M (2015), "An analytic framework for the supercritical Lane-Emden equation and its gradient flow", Int. Math. Res. Not. IMRN. (9), pp. 2342-2385.
BibTeX:
@article{Blatt2015a,
  author = {Blatt, Simon and Struwe, Michael},
  title = {An analytic framework for the supercritical Lane-Emden equation and its gradient flow},
  journal = {Int. Math. Res. Not. IMRN},
  year = {2015},
  number = {9},
  pages = {2342--2385},
  url = {http://dx.doi.org/10.1093/imrn/rnt359},
  doi = {10.1093/imrn/rnt359}
}
Blatt S and Struwe M (2015), "Boundary regularity for the supercritical Lane-Emden heat flow", Calc. Var. Partial Differential Equations. Vol. 54(2), pp. 2269-2284.
BibTeX:
@article{Blatt2015b,
  author = {Blatt, Simon and Struwe, Michael},
  title = {Boundary regularity for the supercritical Lane-Emden heat flow},
  journal = {Calc. Var. Partial Differential Equations},
  year = {2015},
  volume = {54},
  number = {2},
  pages = {2269--2284},
  url = {http://dx.doi.org/10.1007/s00526-015-0865-7},
  doi = {10.1007/s00526-015-0865-7}
}
Blatt S and Reiter P (2015), "Regularity theory for tangent-point energies: the non-degenerate sub-critical case", Adv. Calc. Var.. Vol. 8(2), pp. 93-116.
BibTeX:
@article{Blatt2015c,
  author = {Blatt, Simon and Reiter, Philipp},
  title = {Regularity theory for tangent-point energies: the non-degenerate sub-critical case},
  journal = {Adv. Calc. Var.},
  year = {2015},
  volume = {8},
  number = {2},
  pages = {93--116},
  url = {http://dx.doi.org/10.1515/acv-2013-0020},
  doi = {10.1515/acv-2013-0020}
}
Blatt S and Reiter P (2015), "Towards a regularity theory for integral Menger curvature", Ann. Acad. Sci. Fenn. Math.. Vol. 40(1), pp. 149-181.
BibTeX:
@article{Blatt2015d,
  author = {Blatt, Simon and Reiter, Philipp},
  title = {Towards a regularity theory for integral Menger curvature},
  journal = {Ann. Acad. Sci. Fenn. Math.},
  year = {2015},
  volume = {40},
  number = {1},
  pages = {149--181},
  url = {http://dx.doi.org/10.5186/aasfm.2015.4006},
  doi = {10.5186/aasfm.2015.4006}
}
Blatt S and Reiter P (2013), "Stationary points of O'Hara's knot energies", Manuscripta Math.. Vol. 140(1-2), pp. 29-50.
BibTeX:
@article{Blatt2013,
  author = {Blatt, Simon and Reiter, Philipp},
  title = {Stationary points of O'Hara's knot energies},
  journal = {Manuscripta Math.},
  year = {2013},
  volume = {140},
  number = {1-2},
  pages = {29--50},
  url = {http://dx.doi.org/10.1007/s00229-011-0528-8},
  doi = {10.1007/s00229-011-0528-8}
}
Blatt S (2013), "A note on integral Menger curvature for curves", Math. Nachr.. Vol. 286(2-3), pp. 149-159.
BibTeX:
@article{Blatt2013a,
  author = {Blatt, Simon},
  title = {A note on integral Menger curvature for curves},
  journal = {Math. Nachr.},
  year = {2013},
  volume = {286},
  number = {2-3},
  pages = {149--159},
  url = {http://dx.doi.org/10.1002/mana.201100220},
  doi = {10.1002/mana.201100220}
}
Blatt S (2013), "The energy spaces of the tangent point energies", J. Topol. Anal.. Vol. 5(3), pp. 261-270.
BibTeX:
@article{Blatt2013b,
  author = {Blatt, Simon},
  title = {The energy spaces of the tangent point energies},
  journal = {J. Topol. Anal.},
  year = {2013},
  volume = {5},
  number = {3},
  pages = {261--270},
  url = {http://dx.doi.org/10.1142/S1793525313500131},
  doi = {10.1142/S1793525313500131}
}
Blatt S and Kolasiński Sł (2012), "Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds", Adv. Math.. Vol. 230(3), pp. 839-852.
BibTeX:
@article{Blatt2012,
  author = {Blatt, Simon and Kolasiński, Sławomir},
  title = {Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds},
  journal = {Adv. Math.},
  year = {2012},
  volume = {230},
  number = {3},
  pages = {839--852},
  url = {http://dx.doi.org/10.1016/j.aim.2012.03.007},
  doi = {10.1016/j.aim.2012.03.007}
}
Blatt S (2012), "The gradient flow of the Möbius energy near local minimizers", Calc. Var. Partial Differential Equations. Vol. 43(3-4), pp. 403-439.
BibTeX:
@article{Blatt2012a,
  author = {Blatt, Simon},
  title = {The gradient flow of the Möbius energy near local minimizers},
  journal = {Calc. Var. Partial Differential Equations},
  year = {2012},
  volume = {43},
  number = {3-4},
  pages = {403--439},
  url = {http://dx.doi.org/10.1007/s00526-011-0416-9},
  doi = {10.1007/s00526-011-0416-9}
}
Blatt S (2012), "Boundedness and regularizing effects of O'Hara's knot energies", J. Knot Theory Ramifications. Vol. 21(1), pp. 1250010, 9.
BibTeX:
@article{Blatt2012b,
  author = {Blatt, Simon},
  title = {Boundedness and regularizing effects of O'Hara's knot energies},
  journal = {J. Knot Theory Ramifications},
  year = {2012},
  volume = {21},
  number = {1},
  pages = {1250010, 9},
  url = {http://dx.doi.org/10.1142/S0218216511009704},
  doi = {10.1142/S0218216511009704}
}
Blatt S (2010), "Loss of convexity and embeddedness for geometric evolution equations of higher order", J. Evol. Equ.. Vol. 10(1), pp. 21-27.
BibTeX:
@article{Blatt2010,
  author = {Blatt, Simon},
  title = {Loss of convexity and embeddedness for geometric evolution equations of higher order},
  journal = {J. Evol. Equ.},
  year = {2010},
  volume = {10},
  number = {1},
  pages = {21--27},
  url = {http://dx.doi.org/10.1007/s00028-009-0038-2},
  doi = {10.1007/s00028-009-0038-2}
}
Blatt S (2009), "Chord-arc constants for submanifolds of arbitrary codimension", Adv. Calc. Var.. Vol. 2(3), pp. 271-309.
BibTeX:
@article{Blatt2009,
  author = {Blatt, Simon},
  title = {Chord-arc constants for submanifolds of arbitrary codimension},
  journal = {Adv. Calc. Var.},
  year = {2009},
  volume = {2},
  number = {3},
  pages = {271--309},
  url = {http://dx.doi.org/10.1515/ACV.2009.011},
  doi = {10.1515/ACV.2009.011}
}
Blatt S (2009), "A singular example for the Willmore flow", Analysis (Munich). Vol. 29(4), pp. 407-430.
BibTeX:
@article{Blatt2009a,
  author = {Blatt, Simon},
  title = {A singular example for the Willmore flow},
  journal = {Analysis (Munich)},
  year = {2009},
  volume = {29},
  number = {4},
  pages = {407--430},
  url = {http://dx.doi.org/10.1524/anly.2009.1017},
  doi = {10.1524/anly.2009.1017}
}
Blatt H-P, Blatt S and Luh W (2009), "On a generalization of Jentzsch's theorem", J. Approx. Theory. Vol. 159(1), pp. 26-38.
BibTeX:
@article{Blatt2009b,
  author = {Blatt, Hans-Peter and Blatt, Simon and Luh, Wolfgang},
  title = {On a generalization of Jentzsch's theorem},
  journal = {J. Approx. Theory},
  year = {2009},
  volume = {159},
  number = {1},
  pages = {26--38},
  url = {http://dx.doi.org/10.1016/j.jat.2008.11.016},
  doi = {10.1016/j.jat.2008.11.016}
}
Blatt S and Reiter P (2008), "Does finite knot energy lead to differentiability?", J. Knot Theory Ramifications. Vol. 17(10), pp. 1281-1310.
BibTeX:
@article{Blatt2008,
  author = {Blatt, Simon and Reiter, Philipp},
  title = {Does finite knot energy lead to differentiability?},
  journal = {J. Knot Theory Ramifications},
  year = {2008},
  volume = {17},
  number = {10},
  pages = {1281--1310},
  url = {http://dx.doi.org/10.1142/S0218216508006622},
  doi = {10.1142/S0218216508006622}
}