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Abstract. We consider manifolds M 2n which admit smooth maps into a connected sum of S 1 × S n with only finitely many critical points, for n ∈ {2, 4, 8}, and compute the minimal number of critical points.

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In this paper we use the method of boundary integral equations to treat some transmission problems for Brinkman-type operators on Lipschitz and C 1 domains in Riemannian manifolds.Keywords Brinkman operator · Stokes operator · Lipschitz and C 1 domains · Riemannian manifold · Transmission problem · Layer potentials · Sobolev spaces Mathematics Subject Classifications (2000) 35J25 · 42B20 · 46E35 · 76D · 76M

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