Mathematical Research Letters

Volume 25 (2018)

Number 1

Regularity of envelopes in Kähler classes

Pages: 281 – 289



Valentino Tosatti (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)


We establish the $C^{1,1}$ regularity of quasi-psh envelopes in a Kähler class, confirming a conjecture of Berman.

The author was partially supported by NSF grant DMS-1610278.

Received 20 February 2017

Accepted 16 May 2017

Published 4 June 2018