Abstract

We prove the existence of extremal functions of Sobolev-Poincaré inequality on Sⁿ for p in (1,(1 + ) ∕ 4). For general n-dimensional compact Riemannian manifolds embedded in Rⁿ⁺¹, such an existence result is proved for p in (n ∕ (n − 1),(1 + ) ∕ 4).

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