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- W4300522969 abstract "Let $(M,g)$ be an $n-$dimensional compact Riemannian manifold. Let $h$ be a smooth function on $M$ and assume that it has a critical point $xiin M$ such that $h(xi)=0$ and which satisfies a suitable flatness assumption. We are interested in finding conformal metrics $g_lambda=u_lambda^frac4{n-2}g$, with $u>0$, whose scalar curvature is the prescribed function $h_lambda=lambda^2+h$, where $lambda$ is a small parameter. In the positive case, i.e. when the scalar curvature $R_g$ is strictly positive, we find a family of bubbling metrics $g_lambda$, where $u_lambda$ blows-up at the point $xi$ and approaches zero far from $xi$ as $lambda$ goes to zero. In the general case, if in addition we assume that there exists a non-degenerate conformal metric $g_0=u_0^frac4{n-2}g$, with $u_0>0$, whose scalar curvature is equal to $h$, then there exists a bounded family of conformal metrics $g_{0,lambda}=u_{0,lambda}^frac4{n-2}g$, with $u_{0,lambda}>0$, which satisfies $u_{0,lambda}to u_0$ uniformly as $lambdato 0$. Here, we build a second family of bubbling metrics $g_lambda$, where $u_lambda$ blows-up at the point $xi$ and approaches $u_0$ far from $xi$ as $lambda$ goes to zero. In particular, this shows that this problem admits more than one solution." @default.
- W4300522969 created "2022-10-03" @default.
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- W4300522969 date "2016-12-21" @default.
- W4300522969 modified "2023-10-10" @default.
- W4300522969 title "Large conformal metrics with prescribed scalar curvature" @default.
- W4300522969 hasPublicationYear "2016" @default.
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