Preprints
Blatt S (2016), "Curves between Lipschitz and $ C^1$ and their relation to geometric knot theory", arXiv preprint arXiv:1603.03467.
[BibTeX] |
BibTeX:
@article{blatt2016curves, author = {Blatt, Simon}, title = {Curves between Lipschitz and $ C^1$ and their relation to geometric knot theory}, journal = {arXiv preprint arXiv:1603.03467}, year = {2016} } |
Blatt S (2016), "The Gradient Flow of the Möbius energy: $varepsilon $-regularity and consequences", arXiv preprint arXiv:1601.07023.
[BibTeX] |
BibTeX:
@article{blatt2016gradient, author = {Blatt, Simon}, title = {The Gradient Flow of the Möbius energy: $varepsilon $-regularity and consequences}, journal = {arXiv preprint arXiv:1601.07023}, year = {2016} } |
Blatt S (2009), "Note on continuously differentiable isotopies".
[BibTeX] |
BibTeX:
@misc{Blatt2009e, author = {Blatt, Simon}, title = {Note on continuously differentiable isotopies}, year = {2009}, note = {Preprint Nr. 34, Institut für Mathematik, RWTH Aachen University} } |
Blatt S (2008), "A Lower Bound for the Gromov Distortion of Knotted Submanifolds"
[BibTeX] |
BibTeX:
@unpublished{Blatt2008a, author = {Blatt, Simon}, title = {A Lower Bound for the Gromov Distortion of Knotted Submanifolds}, year = {2008}, note = {Preprint, http://www.instmath.rwth-aachen.de/Preprints/blatt20080808http://www.instmath.rwth-aachen.de/Preprints/blatt20080808} } |
Peer reviewed articles
Blatt S (2017), "Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane--Emden equation", Journal of Differential Equations. Vol. 262(12), pp. 5691-5734. Elsevier.
[BibTeX] |
BibTeX:
@article{Blatt2017, author = {Blatt, Simon}, title = {Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane--Emden equation}, journal = {Journal of Differential Equations}, publisher = {Elsevier}, year = {2017}, volume = {262}, number = {12}, pages = {5691--5734} } |
Blatt S (2017), "The gradient flow of O'Hara's knot energies", Mathematische Annalen., apr, 2017. , pp. 1-69. Springer Nature. |
BibTeX:
@article{Blatt2017a, author = {Blatt, Simon}, title = {The gradient flow of O'Hara's knot energies}, journal = {Mathematische Annalen}, publisher = {Springer Nature}, year = {2017}, pages = {1--69}, doi = {10.1007/s00208-017-1540-4} } |
Blatt S and Struwe M (2016), "Well-posedness of the supercritical Lane--Emden heat flow in Morrey spaces", ESAIM: Control, Optimisation and Calculus of Variations. Vol. 22(4), pp. 1370-1381. EDP Sciences.
[BibTeX] |
BibTeX:
@article{Blatt2016, author = {Blatt, Simon and Struwe, Michael}, title = {Well-posedness of the supercritical Lane--Emden heat flow in Morrey spaces}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP Sciences}, year = {2016}, volume = {22}, number = {4}, pages = {1370--1381} } |
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{Blatt2015, 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, Reiter P and Schikorra A (2015), "Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth", Transactions of the American Mathematical Society. |
Abstract: Motivated by the Coulomb potential of an equidistributed charge on a curve, Jun O'Hara introduced and investigated the first geometric knot energy, the MÃ¶bius energy. We prove that every critical curve of this MÃ¶bius energy is of class and thus extend the corresponding result due to Freedman, He, and Wang for minimizers of the MÃ¶bius energy. |
BibTeX:
@article{Blatt2015a, author = {Blatt, Simon and Reiter, Philipp and Schikorra, Armin}, title = {Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth}, journal = {Transactions of the American Mathematical Society}, year = {2015}, url = {http://www.ams.org/tran/0000-000-00/S0002-9947-2015-06603-3/}, doi = {10.1090/tran/6603} } |
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{Blatt2015b, 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 (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 Struwe M (2015), "Boundary regularity for the supercritical Lane-Emden heat flow", Calculus of Variations and Partial Differential Equations. Vol. 54(2), pp. 2269-2284. Springer.
[BibTeX] |
BibTeX:
@article{Blatt2015d, author = {Blatt, Simon and Struwe, Michael}, title = {Boundary regularity for the supercritical Lane-Emden heat flow}, journal = {Calculus of Variations and Partial Differential Equations}, publisher = {Springer}, year = {2015}, volume = {54}, number = {2}, pages = {2269--2284} } |
Blatt S and Struwe M (2015), "Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow", Calculus of Variations and Partial Differential Equations. Vol. 54(2), pp. 2285-2285. Springer.
[BibTeX] |
BibTeX:
@article{Blatt2015e, author = {Blatt, Simon and Struwe, Michael}, title = {Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow}, journal = {Calculus of Variations and Partial Differential Equations}, publisher = {Springer}, year = {2015}, volume = {54}, number = {2}, pages = {2285--2285} } |
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), "The energy spaces of the tangent point energies", J. Topol. Anal.. Vol. 5(3), pp. 261-270. |
BibTeX:
@article{Blatt2013a, 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 (2013), "A note on integral Menger curvature for curves", Math. Nachr.. Vol. 286(2-3), pp. 149-159. |
BibTeX:
@article{Blatt2013b, 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 (2012), "Boundedness and regularizing effects of O'Hara's knot energies", J. Knot Theory Ramifications. Vol. 21(1), pp. 1-9. |
BibTeX:
@article{Blatt2012, 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 = {1-9}, url = {http://dx.doi.org/10.1142/S0218216511009704}, doi = {10.1142/S0218216511009704} } |
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{Blatt2012a, 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{Blatt2012b, 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 (2010), "Loss of convexity and embeddedness for geometric evolution equations of higher order", Journal of Evolution Equations. Vol. 10(1), pp. 21-27. Springer.
[BibTeX] |
BibTeX:
@article{Blatt2010, author = {Blatt, Simon}, title = {Loss of convexity and embeddedness for geometric evolution equations of higher order}, journal = {Journal of Evolution Equations}, publisher = {Springer}, year = {2010}, volume = {10}, number = {1}, pages = {21--27} } |
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{Blatt2009, 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 (2009), "Chord-arc constants for submanifolds of arbitrary codimension", Adv. Calc. Var.. Vol. 2(3), pp. 271-309. |
BibTeX:
@article{Blatt2009a, 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. Vol. 29(4), pp. 407-430. |
BibTeX:
@article{Blatt2009b, author = {Blatt, Simon}, title = {A singular example for the Willmore flow}, journal = {Analysis}, 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 S and Reiter P (2008), "Does finite knot energy lead to differentiability?", Journal of Knot Theory and Its Ramifications. Vol. 17(10), pp. 1281-1310. World Scientific.
[BibTeX] |
BibTeX:
@article{Blatt2008, author = {Blatt, Simon and Reiter, Philipp}, title = {Does finite knot energy lead to differentiability?}, journal = {Journal of Knot Theory and Its Ramifications}, publisher = {World Scientific}, year = {2008}, volume = {17}, number = {10}, pages = {1281--1310} } |
Proceedings
Blatt S and Reiter P (2014), "How nice are critical knots? Regularity theory for knot energies", Journal of Physics: Conference Series. Vol. 544(1), pp. 012020. |
Abstract: In this note we report on some recent developments in geometric knot theory which aims at finding links between geometric properties of a given knotted curve and its knot type. The central object of this field are so-called knot energies which are defined on closed embedded curves. First we present three important examples of two-parameter knot energy families, namely O'Hara's energies, the (generalized) integral Menger curvature, and the (generalized) tangent- point energies. Subsequently we outline the main steps that lead to C inf -regularity of stationary points- especially minimizers-in the non-degenerate sub-critical range of parameters. Particular attention is devoted to the appearing parallels between these energies which, surprisingly at first glance, are quite similar from an analyst's perspective. |
BibTeX:
@article{Blatt2014, author = {Simon Blatt and Philipp Reiter}, title = {How nice are critical knots? Regularity theory for knot energies}, journal = {Journal of Physics: Conference Series}, year = {2014}, volume = {544}, number = {1}, pages = {012020}, url = {http://stacks.iop.org/1742-6596/544/i=1/a=012020} } |
Blatt S and Reiter P (2014), "Modeling repulsive forces on fibres via knot energies", Molecular Based Mathematical Biology. Vol. 2(1), pp. 29-50. |
BibTeX:
@article{Blatt2014a, author = {Blatt, Simon and Reiter, Philipp}, title = {Modeling repulsive forces on fibres via knot energies}, journal = {Molecular Based Mathematical Biology}, year = {2014}, volume = {2}, number = {1}, pages = {29--50}, doi = {10.2478/mlbmb-2014-0004} } |
Blatt S (2013), "The gradient flow of knot energies.", Oberwolfach Reports. Vol. 10(3), pp. 2119-2153. |
BibTeX:
@article{Blatt2013, author = {Blatt, Simon}, title = {The gradient flow of knot energies.}, journal = {Oberwolfach Reports}, year = {2013}, volume = {10}, number = {3}, pages = {2119--2153}, doi = {10.4171/OWR/2013/37} } |
Blatt S (2013), "The gradient flow of knot energies", Oberwolfach Reports. Vol. 10(2), pp. 1313-1358. |
BibTeX:
@article{Blatt2013a, author = {Blatt, Simon}, title = {The gradient flow of knot energies}, journal = {Oberwolfach Reports}, year = {2013}, volume = {10}, number = {2}, pages = {1313--1358}, doi = {10.4171/OWR/2013/22} } |
Blatt S (2008), "Compactness results for the Ricci flow", Oberwolfach Reports. Vol. 5(4), pp. 2621-2654. |
BibTeX:
@article{Blatt2008, author = {Blatt, Simon}, title = {Compactness results for the Ricci flow}, journal = {Oberwolfach Reports}, year = {2008}, volume = {5}, number = {4}, pages = {2621--2654}, doi = {10.4171/OWR/2008/46} } |