148 research outputs found
Prescribing integral curvature equation
In this paper we formulate new curvature functions on via
integral operators. For certain even orders, these curvature functions are
equivalent to the classic curvature functions defined via differential
operators, but not for all even orders. Existence result for antipodally
symmetric prescribed curvature functions on is obtained. As a
corollary, the existence of a conformal metric for an antipodally symmetric
prescribed curvature functions on is proved. Curvature
function on general compact manifold as well as the conformal covariance
property for the corresponding integral operator are also addressed, and a
general Yamabe type problem is proposed.Comment: References are updated. This is the first paper where the reversed
Hardy-Littlewood-Sobolev inequality is used to solve an equation with
negative critical Sobolev exponen
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