Universal Locally Univalent Functions and Universal Conformal Metrics with Constant Curvature
نویسندگان
چکیده
منابع مشابه
Conformal Metrics with Constant Q-Curvature
We consider the problem of varying conformally the metric of a four dimensional manifold in order to obtain constant Q-curvature. The problem is variational, and solutions are in general found as critical points of saddle type. We show how the problem leads naturally to consider the set of formal barycenters of the manifold.
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Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the...
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We establish compactness for nonnegative solutions of the fourth order constant Qcurvature equations on smooth compact Riemannian manifolds of dimension ≥ 5. If the Q-curvature equals −1, we prove that all solutions are universally bounded. If the Qcurvature is 1, assuming that Paneitz operator’s kernel is trivial and its Green function is positive, we establish universal energy bounds on manif...
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In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M, g) with smooth boundary there exists a metric conformal to g with constant T -curvature, zero Q-curvature and zero mean curvature under generic and conformally invariant assumptions. The problem amounts to solving a fourth order nonlinear elliptic boundary value problem (BVP) with boundary conditions gi...
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2018
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-018-9434-6