Virtual cycles of stable (quasi-)maps with fields

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Relative Compactness and Product Stable Quotient Maps

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Counting Bitangents with Stable Maps

This paper is an elementary introduction to the theory of moduli spaces of curves and maps. As an application to enumerative geometry, we show how to count the number of bitangent lines to a projective plane curve of degree d by doing intersection theory on moduli spaces. AMS Classification 14N35; 14H10, 14C17

Maps With Prescribed Tension Fields

We consider maps into a Riemannian manifold of nonpositive sectional curvature with prescribed tension field. We derive a priori estimates and solve a Dirichlet problem.