Continuity of envelopes of unbounded plurisubharmonic functions

Mårten Nilsson

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

Sammanfattning

On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function ϕ which is continuous in the extended reals on the closure of the domain. For ϕ satisfying certain additional criteria limiting its behavior at the singularities, we establish a set where the Perron–Bremermann envelope Pϕ is guaranteed to be continuous. This result is a generalization of a classic result in pluripotential theory due to J. B. Walsh. As an application, we show that the complex Monge–Ampère equation (ddcu)n=μbeing uniquely solvable for continuous boundary data implies that it is also uniquely solvable for a class of boundary values continuous in the extended reals and unbounded from above.

Originalspråkengelska
Sidor (från-till)3959-3971
Antal sidor13
TidskriftMathematische Zeitschrift
Volym301
Nummer4
DOI
StatusPublished - 2022 aug.

Ämnesklassifikation (UKÄ)

  • Matematisk analys

Fingeravtryck

Utforska forskningsämnen för ”Continuity of envelopes of unbounded plurisubharmonic functions”. Tillsammans bildar de ett unikt fingeravtryck.

Citera det här