Abstract
The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudogradient flows. We show under a mild nondegeneracy assumption the equivalence of both approaches with respect to zero weak limits, in particular a one-to-one correspondence of zero weak limit finite energy subcritical blow-up solutions, zero weak limit critical points at infinity of negative type and sets of critical points with negative Laplacian of the function to be prescribed.
Funding source: Ministero dell’Istruzione, dell’Università e della Ricerca
Award Identifier / Grant number: E83C18000100006
Funding statement: M. Mayer has been supported by the Italian MIUR Department of Excellence grant CUP E83C18000100006.
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Communicated by: Guofang Wang
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