Journal of Symplectic Geometry

Volume 18 (2020)

Number 4

H-principles for regular Lagrangians

Pages: 1071 – 1090



Oleg Lazarev (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


We prove an existence h-principle for regular Lagrangians with Legendrian boundary in arbitrary Weinstein domains of dimension at least six; this extends a previous result of Eliashberg, Ganatra, and the author for Lagrangians in flexible domains. Furthermore, we show that all regular Lagrangians come from our construction and describe some related decomposition results. We also prove a regular version of Eliashberg and Murphy’s h-principle for Lagrangian caps with loose negative end. As an application, we give a new construction of infinitely many regular Lagrangian disks in the standard Weinstein ball.

The author was supported by an NSF postdoc fellowship.

Received 24 January 2019

Accepted 7 July 2019

Published 28 October 2020