"Non UBC"@en .
"DSpace"@en .
"Juan Carlos Fernandez"@en .
"2019-11-05T09:43:09Z"@en .
"2019-05-08T16:55"@en .
"Given an isoparametric function $f$ on the round sphere and\nconsidering the space of functions $w\circ f$, we reduce the Yamabe-type problem\n$$(1)\qquad -\Delta_{g_0}+\lambda u=\lambda |u|^{p-1}u\ \hbox{on}\ \mathbb S^n$$\n with $\lambda>0$ and $p>1$, into a second order singular ODE of the form\n$$w\rq{}\rq{}+{h(r)\over \sin r} w\rq{}+\lambda \left(|w|^{p-1}w-w\right)=0,$$\n with boundary conditions $w\rq{}(0)=0$ and $w\rq{}(\pi)=0$, and where $h$ is a monotone function with exactly one zero\non $[0, \pi]$. Using a double shooting method, for any $k\in\mathbb N$, if $n_1\le n_2$\nare the dimensions of the focal submanifolds determined by $f$ and if $p \in \left(1,\frac{n-n_1+2}{n-n_1-2}\right)$, this problem admits a nodal solution having at least $k$ zeroes.\nThis yields a solution to problem $(1)$ having as nodal set a disjoint union\nof at least $k$ connected isoparametric hypersurfaces. As an application and\nusing that the Hopf fibrations are Riemannian submersions with minimal\nfibers, we give a multiplicity result of nodal solutions to the Yamabe problem\non $\mathbb C P^m$ and on $\mathbb HP^m,$ the complex and quaternionic projective spaces\nrespectively, with $m $ odd.\nThis is a joint work with Jimmy Petean and Oscar Palmas."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72195?expand=metadata"@en .
"40.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: UNAM"@en .
"Banff (Alta.)"@en .
"10.14288/1.0384929"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Postdoctoral"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Partial Differential Equations, Differential Geometry"@en .
"Supercritical problems on the round sphere and the Yamabe problem in projective spaces."@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72195"@en .