Find in Library

In this paper, we classify the complete regular orientable minimal surfaces in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></semantics></math></inline-formula> with total curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>6</mn><mi>π</mi></mrow></semantics></math></inline-formula> and give a method to construct a series of complete non-holomorphic minimal surfaces with total curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>6</mn><mi>π</mi></mrow></semantics></math></inline-formula>. Specially, we give a simplified classification in another method if the surfaces lie in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>4</mn></msup></semantics></math></inline-formula>.