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Prescribing scalar curvature on \(S^ n\) and related problems

Summary: Let \((S^ n,g_ 0)\) be the standard \(n\)-sphere. The following question was raised by L. Nirenberg. Which function \(K(x)\) on \(S^ 2\) is the Gauss curvature of a metric \(g\) on \(S^ 2\) conformally equivalent to \(g_ 0\)? Naturally one may ask a similar question in higher dimensional case, namely which function \(K(x)\) on \(S^ n\) is the ...
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Problème de la courbure scalaire prescrite sur les variétés riemanniennes complètes. (The problem of prescribed scalar curvature for complete Riemannian manifolds)

On a complete Riemannian manifold \((M,g)\) of dimension \(n\geq 3\), the authors study the prescribed scalar curvature problem, that is: Given a \(C^\infty\)-function \(\widetilde f\) on \(M\), there exists a metric \(\widetilde g\), conformal to \(g\), whose scalar curvature coincides with \(\widetilde f\)? This problem has been widely treated in the
Aubin, Thierry, Cotsiolis, Athanase
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The Protein-Folding Problem, 50 Years On

Science, 2012
Ken A Dill, Justin L Maccallum
exaly  

Structure prediction drives materials discovery

Nature Reviews Materials, 2019
Artem Oganov, Chris J Pickard, Qiang Zhu
exaly  

Beyond insecticides: new thinking on an ancient problem

Nature Reviews Microbiology, 2013
Elizabeth A Mcgraw, Scott L O'neill
exaly  

The faint young Sun problem

Reviews of Geophysics, 2012
Georg Feulner
exaly  

Soft Tissue Sarcomas

Ca-A Cancer Journal for Clinicians, 2004
exaly  

Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I

This paper presents results as announced in [C. R. Acad. Sci., Paris, Sér. I 317, No. 2, 159-164 (1993)]. See the review in Zbl 0787.53029.
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