Related papers: Action functionals for strings in four dimensions
It is known that inner functions exist on strongly pseudoconvex domains. In this paper we will show that they exist on a more general type of domains, including some domains of finite type.
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms…
For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…
We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on…
The motion of a charged particle in a straight magnetic field ${\bf B} = B(y)\,\wh{\sf z}$ with a constant perpendicular gradient is solved exactly in terms of elliptic functions and integrals. The motion can be decomposed in terms of a…
Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various power series with coefficients which are polynomials in a…
We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded…
We obtain actions for N D-branes occupying points in a manifold with arbitrary Kahler metric. In one complex dimension, the action is uniquely determined (up to second order in commutators) by the requirement that it reproduce the masses of…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an…
In the present paper, we study timelike surfaces free of minimal points in the four-dimensional Minkowski space. For each such surface we introduce a geometrically determined pseudo-orthonormal frame field and writing the derivative…
An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential in obtaining a macroscopic description of dislocation…
We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable…
The four-point function arising in the scattering of closed bosonic strings in their tachyonic ground state is evaluated on a surface of infinite genus. The amplitude has poles corresponding to physical intermediate states and divergences…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…
The effective action for 2d-gravity with manifest area-preserving invariance is obtained in the flat and in the general gravitational background. The cocyclic properties of the last action are proved, and generalizations on higher…
We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…