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A maximum principle for compressible flow on a surface

1978
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Proceedings of the American Mathematical Society
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We show that the speed of a steady, irrotational, subsonic now on a surface cannot attain its maximum at a point of positive Gauss curvature. In his work on curvature and homology, Bochner [3] obtained a formula for the Laplacian of the norm of a harmonic form on an orientable Riemannian manifold in terms of the curvature of the manifold. In this paper we obtain a corresponding formula for p-harmonic forms which describe compressible flows and will use this result to show that a steady,

doi:10.1090/s0002-9939-1978-0482795-2
fatcat:lazlyrbfxfhubacck7cywbhjtu