Related papers: Seiberg-Witten Equations on R^8
In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in $1$D. The proof is based on the virial estimate which provides local in space average decay of bounded small…
The Seiberg-Witten equations are defined on certain complex line bundles over smooth oriented four manifolds. When the base manifold is a complex Kahler surface, the Seiberg-Witten equations are essentially the Abelian vortex equations.…
We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of $S^1 \times S^3$. The invariant has two terms; one is a count of solutions to the Seiberg-Witten equations on X, and the other…
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107--113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of…
It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordstrom black hole background; in particular, there are no static solutions of the Dirac equation in such a background field. The…
We derive the global properties of static spherically symmetric solutions to the Einstein-Maxwell-dilaton system in the presence of an arbitrary exponential dilaton potential. We show that -- with the exception of a pure cosmological…
In this paper, we first establish an $S^1$-equivariant index theorem for Spin$^c$ Dirac operators on $\mathbb{Z}/k$ manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198},…
We exploit the Seiberg -- Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space time. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the…
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift-Hohenberg…
We consider the Swift-Hohenberg equation on manifolds with conical singularities and show existence, uniqueness and maximal regularity of the short time solution in terms of Mellin-Sobolev spaces. Moreover, we give a necessary and…
We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum…
In this paper we construct the Seiberg-Witten maps for superfields on the theta-theta deformed superspaces with N=(1/2,0) and N=(1/2,1/2) supersymmety. We show that on the N=(1/2,0) deformed superspace there is no Seiberg-Witten map for…
We show novel types of uniqueness and rigidity results for Schr\"odinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution $u=0$ is the only…
We consider the Schr\"odinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-symmetric solutions for the homogeneous equations for certain…
The cubic complex one-dimensional Ginzburg-Landau equation is considered. Using the Hone's method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing…
In this thesis we prove analytic results about a cohomotopical Seiberg-Witten theory for a Riemannian, Spin$^c$(4), 4-manifold with periodic ends, $(X, g, {\tau})$ . Our results show that, under certain technical assumptions on $(X, g,…
We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…
We prove sharp Strichartz estimates for the semi-classical Schrodinger equation on a compact manifold with smooth, strictly geodesically concave boundary. We deduce sharp (classical) Strichartz estimates for the Schrodinger equation outside…
We prove non-uniqueness of weak solutions to the forced $\alpha$-SQG equation with Sobolev regularity $W^{s,p}$ in the supercritical regime $s < \alpha + \frac{2}{p}$, covering the 2D Euler equation ($\alpha = 0$), the Surface…
In this paper we pursue further a programme initiated in a previous work and aimed at the construction, classification and property investigation of time dependent solutions of supergravity (superstring backgrounds) through a systematic…