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 May 2018


Let(M, g)#(M ,g)be a twosided asymptotically flat hypersurfaceas above. LetΓ֒→Mbe a smooth, compact inner boundary lying on some totallygeodesic hypersurfaceP ֒→Mand assume that, alongΓ,Mis orthogonal toP.Then, if orientations are fixed as above,mg=mh−cn∫Γ〈X, η〉s1(N)dΓ ++cn∫M(2S2ΘX+ Ricg(N,XT))dM,(1.10)wheres1(N)is the mean curvature ofΓ֒→Pwith respect toN,ηis the exteriorunit conormal toM,S2is the2mean curvature ofM(see (2.2) below) andXTis the tangential component ofXalongM.
