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We prove that all proper rigid-analytic spaces with \enough" algebraically independent meromorphic functions are algebraic (in the sense of proper algebraic spaces). This is a non-archimedean analogue...
Enumerative Geometry on Enriques surfaces.
Generalized complex geometry and topological sigma-models.
In [JM02, section 14], Ji and MacPherson give new constructions of the Borel--Serre and reductive Borel--Serre compactifications [BS73, Zuc82] of a locally symmetric space. They use equivalence classe...
The Grassmannian space GC(2, 4) embedded in CP5 as the Klein quadric of twistor theory has a natural interpretation in terms of the geometry of “round” 2-spheres in S4. The incidence of two lines in C...
Let T (S) be the Teichm¨uller space of a hyperbolic Riemann surface S and let Belt(S) be the Banach space of bounded measurable Beltrami differentials μ = μdz/dz on S with L∞-norms. Suppose M(...
We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides wi...
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
In this artile we review some reent work on fourth order equations in onformal geometry of three and four dimensions. We dis uss some an existene result for a Yamabe-type equation in dimension three. ...
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal...
In this paper we describe our current research in the theory of partial di erential equations in conformal geometry. We introduce a bubble tree structure to study the degeneration of a class of Yamabe...
In this paper, we prove an uniqueness theorem for a n-th order elliptic equation on the standard n-sphere Sn. The problem arises naturally from the point of view of conformal geometry. The method we u...

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