Classical Schwarz reflection principle for Jenkins–Serrin type minimal surfaces
Classical Schwarz reflection principle for Jenkins–Serrin type minimal surfaces
Abstract We give a proof of the classical Schwarz reflection principle for Jenkins–Serrin type minimal surfaces in the homogeneous three manifolds $$\mathbb E(\kappa ,\tau )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>κ</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> for $$\kappa \leqslant 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>κ</mml:mi><mml:mo>⩽</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> and $$\tau \geqslant 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>τ</mml:mi><mml:mo>⩾</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> . In our previous paper, we proved a reflection principle in …