Palais Leaf-Space Manifolds and Surfaces Carrying Holomorphic Flows

SYMPLECTIC SURFACES AND GENERIC j-HOLOMORPHIC STRUCTURES ON 4-MANIFOLDS

It is a well known fact that every embedded symplectic surface Σ in a symplectic four-manifold (X4, ω) can be made J-holomorphic for some almost-complex structure J compatible with ω. In this paper we investigate when such a structure J can be chosen generically in the sense of Taubes. The main result is stated in Theorem 1.2. As an application of this result we give examples of smooth and non-...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

Discrete Curvature Flows for Surfaces and 3-Manifolds

Intrinsic curvature flows can be used to design Riemannian metrics by prescribed curvatures. This chapter presents three discrete curvature flow methods that are recently introduced into the engineering fields: the discrete Ricci flow and discrete Yamabe flow for surfaces with various topology, and the discrete curvature flow for hyperbolic 3manifolds with boundaries. For each flow, we introduc...

Holomorphic discs and sutured manifolds

In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds and links. Our invariant is unchanged under product decompositions and is zero for nontaut sutured manifolds. As an application, an invariant of Seifert surfaces is given and is computed in a few i...

Holomorphic Submersions from Stein Manifolds