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A class of variational functionals in conformal geometry
A class of variational functionals in conformal geometry
2014/4/3
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...
On a fully non-linear elliptic PDE in conformal geometry
Fully nonlinear PDE generalized Yamabe problem
2014/4/3
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. ...
Fractional Laplacian in conformal geometry
Conformal geometry Fractional Laplacian Conformally covariant operators Dirichlet-to-Neumann operators Asymptotically hyperbolic manifolds
2014/4/3
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...
ON UNIQUENESS OF SOLUTION OF A n-TH ORDER DIFFERENTIAL EQUATION IN CONFORMAL GEOMETRY
ON UNIQUENESS OF SOLUTION A n-TH ORDER DIFFERENTIAL EQUATION CONFORMAL GEOMETRY
2014/4/3
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...
The work is collaborated with Shing-Tung Yau, Feng Luo, Tony
Chan, Paul Thompson, Yalin Wang, Ronald Lok Ming Lui, Hong
Qin, Dimitris Samaras, Jie Gao, Arie Kaufman, and many other
mathematicians, ...
Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE
Conformal geometry of surfaces Lagrangian--Grassmannian and second order PDE
2010/12/1
Of all real Lagrangian{Grassmannians LG(n; 2n), only LG(2; 4) admits a distinguished Lorentzian) conformal structure and hence is identi ed with the inde nite Mobius space S1;2.
A theorem of Lawson and Simons states that the only stable minimal submanifolds in CPn are complex submanifolds. We generalize their result to the cases of HPn and OP2. Our approach gives a unified vi...
Local Estimates for Some Elliptic Equations Arising from Conformal Geometry
Local Estimates Elliptic Equations Arising Conformal Geometry
2018/4/19
We present some local gradient and Hessian estimates from C0 estimates for some elliptic equations arising from conformal deformations on the manifolds with totally geodesic boundary, which generalize...
Nonlinear elliptic equations in conformal geometry
Nonlinear elliptic equations conformal geometry
2014/4/3
This is the set of Nachdiplom lectures which I have given during April-July 2001 at Zurich. In the lectures, I have focused the study on some non-linear partial di erential equations related to curvat...