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We consider a process on a compact two-dimensional surface which consists of the fast motion along the stream lines of an incompressible periodic vector eld perturbed by white noise. It gives rise ...
The work of Fricke-Klein [20] develops the deformation theory of hyperbolic structures on a surface Σ in terms of the space of representations of its fundamental group damental group π = π1(Σ) in SL(...
A generalization of Blaschke’s Rolling Theorem for not necessarily convex sets is proved that exhibits an intimate connection between a generalized notion of convexity, various concepts in mathematic...
We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bun...
Given a Lagrangian sphere in a symplectic 4-manifold (M, ω) with b+ = 1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension of (M, ω) is −∞, this result t...
In this article we study the period map for a family of K3 surfaces which is given by the anticanon-ial divisor of a toric variety. We determine the period di erential equation and its monodromy group...
This paper extends parts of the results from [14] for plane curves to the case of surfaces in Rn. Let M be a compact connected oriented manifold of dimension less than n without boundary. Then shape s...
The equation ∂2 ∂z∂¯z log(s2) = |Q|2s−4 + s2 (1.1) is satisfied by the conformally flat metric s2|dz|2 of a minimal Lagrangian surface in the complex hyperbolic plane CH2,...
In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator $C_{\rho }$ is...

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