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- W2294642822 abstract "Let $(M,g)$ be a compact smooth connected Riemannian manifold (without boundary) of dimension $Nge7$. Assume $M$ is symmetric with respect to a point $xi_0$ with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem $$(P_epsilon)qquad-mathcal L_g u+epsilon u=u^{N+2over N-2} hbox{in} (M,g) .$$ We prove that for any $kin mathbb N$, there exists $epsilon_k>0$ such that for all $epsilonin (0, epsilon_k)$ the problem $(P_epsilon)$ has a symmetric solution $u_epsilon ,$ which looks like the superposition of $k$ positive bubbles centered at the point $xi_0$ as $epsilonto 0$. In particular, $xi_0$ is a {em towering} blow-up point." @default.
- W2294642822 created "2016-06-24" @default.
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- W2294642822 date "2016-03-04" @default.
- W2294642822 modified "2023-09-23" @default.
- W2294642822 title "Towering phenomena for the Yamabe equation on symmetric manifolds" @default.
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