Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space

摘要: equipped with the hyperbolic metric y-Z(dxZ+dy2). A standard compactification of IH involves adding boundary (R"• {0})w {*} so that I[-I is simply one point Euclidean closed half-space R" • [0, ~). Suppose 0 7, any interior singularities M must remain in a bounded region space. Near points F (in topology), w may thus be described as graph function. This function solution an interesting partial differential equation becomes degenerate along part corresponding to F. The second author has recently established [L] higher-regularity result for this equation, which implies, particular, r if cgk,~ k=2 , 3 .... ~ . Finally, case bounds star-