Construction of Quaternary Stereocenters by Palladium‐Catalyzed Carbopalladation‐Initiated Cascade Reactions

The enantioselective synthesis of molecules containing quaternary stereocenters is a field of intense research interest and development. Among the known organic transformations, carbopalladation‐initiated domino transformations constitutes a general method for the construction of compounds containing cyclic or spiro quaternary stereocenters. In this Minireview, recent achievements in palladium‐catalyzed domino Heck/C?H functionalizations and developments in enantioselective carbopalladation‐initiated domino processes are summarized.     

Copper‐Catalyzed Enantioselective Construction of Tertiary Propargylic Sulfones

Tertiary propargylic sulfones are of significant importance in organic synthesis and medicinal chemistry, but to date no general asymmetric synthesis approach has been developed. We disclose a versatile copper‐catalyzed sulfonylation of propargylic cyclic carbonates using sodium sulfinates that allows the construction of propargylic sulfones featuring elusive quaternary stereocenters. This method provides the first successful example of such an enantioselective propargylic sulfonylation, features high asymmetric induction, wide functional group tolerance, and scalability, and enables attractive product diversification.     

Open problems in pluripotential theory

We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold setting.     

Boundary value problems for mixed type equations and applications

In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is then used to study a particular class of fully nonlinear mixed type equations which arise in applications to differential geometry.     

A note on the contact angle boundary condition for Monge-Ampère equations

We give a simple proof of a result of Xinan Ma concerning a necessary condition for the solvability of the two-dimensional Monge-Ampère equation subject to the contact angle or capillarity boundary condition. Our technique works for more general Monge-Ampère equations in any dimension, and also extends to some other boundary conditions.