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ESSENTIAL KILLING FIELDS OF PARABOLIC GEOMETRIES: PROJECTIVE AND CONFORMAL STRUCTURES
PARABOLIC GEOMETRIES PROJECTIVE
2015/10/14
We use the general theory developed in our article [1]
in the setting of parabolic geometries to reprove known results on
special in nitesimal automorphisms of projective and conformal
geometries.
CONFORMAL ACTIONS OF NILPOTENT GROUPS ON PSEUDO-RIEMANNIAN MANIFOLDS
CONFORMAL ACTIONS PSEUDO-RIEMANNIAN MANIFOLDS
2015/10/14
We study conformal actions of connected nilpotent Lie groups
on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q)
compact manifold M supports a conformal action of a connected nilpo...
Conformal Triality and AdS/CFT 3 Correspondence
Conformal Triality AdS/CFT 3 Correspondence
2015/3/19
Conformal Triality and AdS/CFT 3 Correspondence.
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...
CONFORMAL INVARIANTS ASSOCIATED TO A MEASURE: CONFORMALLY COVARIANT OPERATORS
CONFORMAL INVARIANTS ASSOCIATED MEASURE CONFORMALLY COVARIANT OPERATORS
2014/4/3
In this paper we study Riemannian manifolds (Mn, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling...
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 A CONFORMAL GAP AND FINITENESS THEOREM FOR A CLASS OF FOUR MANIFOLDS
ON A CONFORMAL GAP FINITENESS THEOREM CLASS OF FOUR MANIFOLDS
2014/4/3
In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree st...
In this note we study some conformal invariants of a Riemannanian manifold (Mn;g) equipped with a smooth measure m. In particular, we show that there is a natural de nition of the Ricci and scalar cur...
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, ...
Maximization of the second conformal eigenvalue of spheres
Maximization the second conformal eigenvalue spheres Spectral Theory
2012/6/14
We establish in this paper an upper bound on the second eigenvalue of n-dimensional spheres in the conformal class of the round sphere. This upper bound holds in all dimensions and is asymptotically s...
Dimensions of average conformal repeller
Hausdorff dimension Non-conformal repellers Topological pressure
2011/10/19
In this paper, average conformal repeller is defined, which is generalization of conformal repeller. Using thermodynamic formalism for sub-additive potential defined in [5],Hausdorff dimension and box...