KOHN–ROSSI COHOMOLOGY AND ITS APPLICATION TO THE COMPLEX PLATEAU PROBLEM, III Rong Du & Stephen Yau Abstract

More precisely we construct the SYZ mirror of a neighborhood of an anti-canonical toric divisor in a toric Calabi–Yau manifolds of infinite-type, which contains the

Our tools include Berkovich spaces, tropical geometry, Gromov- Witten theory and the GAGA theorem for non-archimedean analytic

The outline of the paper is as follows: in Section 2, some preliminaries are given, almost-K¨ ahler potentials are defined and uniqueness for the Calabi-Yau equation is proved;

The following theorem is a fundamental theorem toward the com- plete solution of the classical complex Plateau problem for 3-dimensional strongly pseudoconvex Calabi-Yau CR manifold

In [5] and [16], many complete intersection Calabi–Yau 3-manifolds in toric varieties were verified to be connected by extremal transitions, which include Calabi–Yau hypersurfaces

The following beautiful theorem of Harvey and Lawson connects the theory of strongly pseudoconvex CR mani- folds on the one hand and the theory of normal isolated singularities on

For example, Donaldson-Thomas invariants that we mentioned earlier and that originally were introduced via gauge theory, nowadays are actually more widely regarded as part of

This might seem very different from what we are considering here, where the complex structure is fixed and the K¨ ahler class degenerates, but in the case when the Calabi-Yau