An upper bound of the total Q-curvature and its isoperimetric deficit for higher-dimensional conformal Euclidean metrics

Ndiaye, C. B.; Xiao, J.
May 2010
Calculus of Variations & Partial Differential Equations;May2010, Vol. 38 Issue 1/2, p1
Academic Journal
The aim of this paper is to give not only an explicit upper bound of the total Q-curvature but also an induced isoperimetric deficit formula for the complete conformal metrics on Rn, n = 3 with scalar curvature being nonnegative near infinity and Q-curvature being absolutely convergent.


Related Articles

  • The relative isoperimetric inequality outside convex domains in R n . Choe, Jaigyoung; Ghomi, Mohammad; Ritor�, Manuel // Calculus of Variations & Partial Differential Equations;Aug2007, Vol. 29 Issue 4, p421 

    We prove that the area of a hypersurface S which traps a given volume outside a convex domain C in Euclidean space R n is bigger than or equal to the area of a hemisphere which traps the same volume on one side of a hyperplane. Further, when C has smooth boundary ? C, we show that equality...

  • Eigenvalues of Euclidean wedge domains in higher dimensions. Ratzkin, Jesse // Calculus of Variations & Partial Differential Equations;Sep2011, Vol. 42 Issue 1/2, p93 

    In this paper, we use a weighted isoperimetric inequality to give a lower bound for the first Dirichlet eigenvalue of the Laplacian on a bounded domain inside a Euclidean cone. Our bound is sharp, in that only sectors realize it. This result generalizes a lower bound of Payne and Weinberger in...

  • Necessary and sufficient conditions for local Pareto optimality on time scales. Malinowska, A. B.; Torres, D. F. M. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 6, p803 

    We study a multiobjective variational problem on time scales. For this problem, necessary and sufficient conditions for weak local Pareto optimality are given. We also prove a necessary optimality condition for the isoperimetric problem with multiple constraints on time scales.

  • Finite-Gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations. Calini, A.; Ivey, T. // Journal of Nonlinear Science;Dec2007, Vol. 17 Issue 6, p527 

    We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is �unpinched� to produce a new...

  • Isoperimetric comparison theorems for manifolds with density. Maurmann, Quinn; Morgan, Frank // Calculus of Variations & Partial Differential Equations;Sep2009, Vol. 36 Issue 1, p1 

    We give several isoperimetric comparison theorems for manifolds with density, including a generalization of a comparison theorem from Bray and Morgan. We find for example that in the Euclidean plane with radial density exp(r a) for a = 2, discs about the origin minimize perimeter for given area,...

  • An isoperimetric problem for tetrahedra. Zalgaller, V. // Journal of Mathematical Sciences;Jan2007, Vol. 140 Issue 4, p511 

    It is proved that a regular tetrahedron has the maximal possible surface area among all tetrahedra having surface with unit geodesic diameter. An independent proof of O’Rourke-Schevon’s theorem about polar points on a convex polyhedron is given. A. D. Aleksandrov’s general...

  • Isoperimetric balls in cones over tori. Morgan, Frank // Annals of Global Analysis & Geometry;Apr2009, Vol. 35 Issue 2, p133 

    In the cone over a cubic three-torus T3, balls about the vertex are isoperimetric if the volume of T3 is less than π/16 times the volume of the unit three-sphere. The conjectured optimal constant is 1.

  • ON SOME GENERALIZATION OF THE WILLMORE FUNCTIONAL FOR SURFACES IN…. BERDINSKY, D. A. // Sibirskie Elektronnye Matematicheskie Izvestiia;2010, Vol. 7, p140 

    We propose some generalization of the Willmore functional for closed surfaces in….We discuss the relation between this functional and isoperimetric problem in ….

  • On the L p intersection body. Xian-yang Zhu; Gang-song Leng // Applied Mathematics & Mechanics;Dec2007, Vol. 28 Issue 12, p1669 

    In this paper, by using the Brunn-Minkowski-Firey mixed volume theory and dual mixed volume theory, associated with L p intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate forms are established for L p intersection body about the normalized L p ...


Read the Article


Sign out of this library

Other Topics