Characterization of The Algebraic Surfaces on Which The Classical Phragmen-Lindelof Theorem Holds Using Branch Curves
- Resource Type
- Authors
- A Rudiger W. Braun; B. A. Taylor; Reinhold Meise
- Source
- Pure and Applied Mathematics Quarterly. 7:139-197
- Subject
- Algebraic cycle
Phragmén–Lindelöf principle
Combinatorics
Intersection theory
medicine.medical_specialty
Plurisubharmonic function
General Mathematics
Bounded function
Algebraic surface
Real algebraic geometry
medicine
Algebraic variety
Mathematics
- Language
- ISSN
- 1558-8602
1558-8599
Let V be an algebraic variety in C. We say that V satisfies the strong PhragmenLindelof property (SPL) or that the classical Phragmen-Lindelof Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z| + o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. We characterize the algebraic surfaces V in C which satisfy (SPL) by using the behavior of their branch curves with respect to many projections in C which are noncharacteristic for V at infinity.