相关论文: Holomorphic Curves and Toda Systems
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
We construct coordinates on conjugacy classes of traceless complex matrices with simple spectrum that diagonalize the non-periodic Toda vector field. By this we mean that the coordinates, defined on an open and dense neighborhood of any…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how to use this treatment to construct a special basis in every space of conformal…
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
In this paper, we study the problem of computing a homotopy from a planar curve $C$ to a point that minimizes the area swept. The existence of such a minimum homotopy is a direct result of the solution of Plateau's problem. Chambers and…
Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, two- and three-point couplings known in Liouville…
This paper studies solutions to a singular $SU(3)$ Toda system with linear source terms on a compact Riemann surface $\Sigma$ with smooth boundaries $\partial\Sigma$. We establish the existence of solutions when the parameters are not…
We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin to…
A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the…
We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…
Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair…
We study complex analytic projective connections on surfaces in projective n-spaces in terms of the "second" neighborhood of the surface in the ambient space, and in terms of the osculating behavior of the integral curves. We also…
We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain…
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld…
A projective hypersurface is nodal if it does not have singularities worse than simple nodes. We calculate the rational cohomology of the spaces of equations of nodal cubic and quartic plane curves and also nodal cubic surfaces in the…
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface $\Sigma$, including the minimum number of self-intersections, the minimum length of the words representing them in a…
We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves, $a^2b^n$ ($n\ge 3$), on a complete one-holed hyperbolic torus in its relative…
We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi…