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Morse theory and a scalar field equation on compact surfaces

By A. Malchiodi


he aim of this paper is to study a nonlinear scalar field equation on a surface Σ via a Morse-theoretical approach, based on some of the methods in [25]. Employing these ingredients, we derive an alternative and direct proof (plus a clear interpretation) of a degree formula obtained in [18], which used refined blow-up estimates from [34] and [17]. Related results are derived for the prescribed Q-curvature equation on four manifolds

Publisher: Khayyam Publishing Company, Inc.
Year: 2008
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