Kähler metrics of constant scalar curvature on bundles over CPn-1.
Heat flows for extremal Kähler metrics
Let be a closed polarized complex manifold of Kähler type. Let be the maximal compact subgroup of the automorphism group of . On the space of Kähler metrics that are invariant under and represent the cohomology class , we define a flow equation whose critical points are the extremal metrics,those that minimize the square of the -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its only...
The super complex Frobenius theorem
We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Codimension two transcendental submanifolds of projective space
We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
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