Review of geometry and analysis

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The classical theory of minimal surfaces (2011, background): “The problem of understanding the relation between the intrinsic notion of completeness and the extrinsic one of properness is known as the embedded Calabi-Yau problem in minimal surface theory, see [13], [21], [209], [210] and [151] for the original Calabi-Yau problem in the complete immersed settin”
Isometric Immersions and Compensated Compactness (2008, unknown): “Yau [40]; also see [21,34,36]).”
An extension of Barta’s Theorem and geometric applications (2003, background): “r)), (7) where BNm(c)(r) is the geodesic ball with radius rin Nn(c). Equality in (7) holds iﬀ Ω = BNm(c)(r) and BN n(c)(p,r) ≡ BN (c)(r). After Nadirashvili’s [15] bounded minimal surfaces in R3, Yau [18] asked about the spectrum of a Nadirashvili minimal surface, in particular he asked if it were d”
Hyperbolic Mean Curvature Flow (2010, background): “A natural problem is as follows: in the above argument if we replace the velocity dX dt by the acceleration d (2)X dt(2) , what happens? In fact, Yau in [15] has suggested the following equation related to a vibrating membrane or the motion of a surface d(2)X dt(2) = H~n, (1.”