Restriction theorems for a surface with negative curvature

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On the multilinear restriction and Kakeya conjectures (2005, background): “In recent years certain bilinear analogues of the restriction problem have come to light in natural ways from a number of sources (see for example [10], [19], [23], [31], [35], [28], [29], [32], [20], [14] concerning the well-posedness theory of non-linear dispersive equations, and applications to a”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “ry; in particular, whether S1 and S2 intersect is not relevant here. 4This conjecture is known to be false for surfaces with nonvanishing curvatures of diﬀerent sign, such as the saddle; see [35] and [53]. 5Following the d= 3 case in Moyua, Vargas and Vega [38]. ASPECTS OF MULTILINEAR HARMONIC ANALY”
Bilinear restriction estimates for surfaces with curvatures of different signs (2005, unknown): “Vargas [18] independently obtained Corollary 1.”
Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, methodology): “The sharp bilinear restrict estimates were first proven by Tao [20] for elliptic surfaces and later these was extended to more general surfaces by the author [10] and Vargas [25].”