Die Korrespondenz mit Jacob Taubes 1952

Taubes, Susan; Taubes, Jacob; Weigel, Sigrid; Taubes, Tanaquil; Taubes, Ethan; Huber, Evi Ziegler c/o EDV Fotowerk

doi:10.30965/9783846755976

Cited by 16 publications

(6 citation statements)

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“…In particular, we show that such a function is globally bounded on M (or on a compact region, if the manifold itself is not compact). This strategy is well-known for second order elliptic operators on scalar functions, see [20,40] and references therein, as well as [44,28] for the spinorial case. However, here, inspired by [24], we choose to use a version of frequency function which is slightly different from the one typically used in the mentioned references on Dirac equations.…”

Section: A Frequency Function For Spinorsmentioning

confidence: 99%

“…The zero loci of the spinors, or more generally those of Z 2 -harmonic spinors, were analyzed in depth already by [22,28,44] etc.…”

Section: Introductionmentioning

confidence: 99%

“…For harmonic functions, this corresponds to the frequency function used by Almgren in [1] to study minimal submanifolds. The choice of the particular form of frequency function N px, rq is partially inspired from [24], meanwhile there are other formulation of frequency functions for spinors solving various Dirac-type equations, see [22,28,44] and the references therein. The most significant property of the frequency function (1.6), for our purposes, is the contained in the following result.…”

Section: Introductionmentioning

confidence: 99%

“…In lower dimension, say dimension two, three and four, the zero loci of spinor solutions are geometrically significant and have rather nice structural properties, see e.g. [28,44]. However, it is unclear how to provide a similar description in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

Borrelli

2017

Journal of Differential Equations

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In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |ψ| 2 ψ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H 1 2 (R 2 , C 2 ) → L 4 (R 2 , C 4 ) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments.

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Section: A Frequency Function For Spinorsmentioning

confidence: 99%

“…The zero loci of the spinors, or more generally those of Z 2 -harmonic spinors, were analyzed in depth already by [22,28,44] etc.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

Borrelli

2017

Journal of Differential Equations

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“…* The proof presented here was partly inspired by some proficient calculations by Clifford Taubes[Tau5].…”

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confidence: 99%

On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces

Tanaka

2018

Geom Dedicata

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This article finds a structure of singular sets on compact Kähler surfaces, which Taubes introduced in the studies of the asymptotic analysis of solutions to the KapustinWitten equations and the Vafa-Witten ones originally on smooth four-manifolds. These equations can be seen as real four-dimensional analogues of the Hitchin equations on Riemann surfaces, and one of common obstacles to be overcome is a certain unboundedness of solutions to these equations, especially of the "Higgs fields". The singular sets by Taubes describe part of the limiting behaviour of a sequence of solutions with this unboundedness property, and Taubes proved that the real two-dimensional Haussdorff measures of these singular sets are finite. In this article, we look into the singular sets, when the underlying manifold is a compact Kähler surface, and find out that they have the structure of an analytic subvariety in this case.

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Heidegger and His Jewish Reception

Herskowitz¹

2020

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Die Korrespondenz mit Jacob Taubes 1952

Cited by 16 publications

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Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces

Heidegger and His Jewish Reception

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