List of publications

## Preprints

 Blatt S (2016), "The Gradient Flow of O'Hara's Knot Energies", January, 2016. [Abstract] [BibTeX] [URL] 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] [BibTeX] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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] [DOI] [URL] 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} }