Abstract

GARCIA CAMACHO, Gonzalo  and  POSADA VERA, Liliana. rev. cienc. [online]. 2015, vol.19, n.1, pp.73-86. ISSN 0121-1935.

This paper considers the prescribed scalar curvature problem on the sphere for n = 3. Given a prescribed scalar curvature function K : Sn ? R and a centered dilation defined by Fy = ∑-1 o Dβ o ∑, y ? Bn+1, where ∑ is the stereographic projection and Dβ is a dilation in ℝn, in this work we estimate the gradient of the function K near the critical point of the function We will use this estimate to find Lp estimates of the first two y-derivatives of the function K o Fy (ξ)

Keywords : metrics; scalar curvature; conformal geometry.

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