On a conformally invariant variational problem on differential forms

✍ Scribed by Wei Wang

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 368 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.11.039

✦ Synopsis

We consider a conformally invariant constrained variational problem on p differential forms for p < dim M-2 2 coming from conformal geometry and the associated Yamabe-type system of partial differential equations. It is shown that the infimum λ p (M) of the functional is not bigger than λ p (R n ) and if λ p (M) < λ p (R n ), then λ p (M) is achieved by a C 2+ p-form for some > 0.