Abstract
Using the strong maximum principle, we obtain a constant rank theorem for the k-convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k-convex starshaped hypersurface with prescribed mean curvature in R n+1.
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Communicated by C. S. Lin.
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Han, F., Ma, XN. & Wu, D. The existence of k-convex hypersurface with prescribed mean curvature. Calc. Var. 42, 43–72 (2011). https://doi.org/10.1007/s00526-010-0379-2
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DOI: https://doi.org/10.1007/s00526-010-0379-2