The region of the unit Euclidean sphere that admits a class of (r, s)-linear Weingarten hypersurfaces
Marco Antonio Lázaro Velásquez
Abstract:In the unit Euclidean sphere Sn+1, we deal with a class of hypersurfaces that were characterized in [23] as the critical points of a variational problem, the so-called (r, s)-linear Weingarten hypersurfaces (0 ≤ r ≤s ≤ n−1); namely, the hypersurfaces of Sn+1 that has a linear combination arHr+1+...+asHs+1 of their higher order mean curvatures Hr+1 and Hs+1 being a real constant, where ar,..., ar are nonnegative real numbers (with at least one non zero). By assuming a geometric constraint involving the higher o… Show more
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