We show that timelike minimal cylinders in flat Minkowski space R^(1+n) always develop singularities if n = 2, as recently proved by L. Nguyen and G. Tian, are generically regular if n > 3, and exibit an intermediate behavior when n = 3. The proofis based on the use of the so-called orthogonal gauge for parametrizing timelike minimalcylinders.
On the regularity of timelike extremal surfaces
ORLANDI, Giandomenico
2015-01-01
Abstract
We show that timelike minimal cylinders in flat Minkowski space R^(1+n) always develop singularities if n = 2, as recently proved by L. Nguyen and G. Tian, are generically regular if n > 3, and exibit an intermediate behavior when n = 3. The proofis based on the use of the so-called orthogonal gauge for parametrizing timelike minimalcylinders.
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