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Let $(M,g)$ be any closed Riemannianan manifold and $(N,h)$ be a Riemannian manifold of constant positive scalar curvature. We prove that the Yamabe equation on the Riemannian product $(M\times N… Click to show full abstract
Let $(M,g)$ be any closed Riemannianan manifold and $(N,h)$ be a Riemannian manifold of constant positive scalar curvature. We prove that the Yamabe equation on the Riemannian product $(M\times N , g + \delta h)$ has at least $Cat(M) +1 $ solutions for $\delta$ small enough, where $Cat(M)$ denotes the Lusternik-Schnirelmann-category of $M$. Cat(M) of the solutions obtained have energy arbitrarily close to the minimum.
Keywords:
equation lusternik;
results yamabe;
yamabe equation;
lusternik schnirelmann;
multiplicity results
Journal Title: Journal of Functional Analysis
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Functional Analysis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!