Classification of Complete Regular Minimal Surfaces in ℝ<i><sup>n</sup></i> with Total Curvature −6<i>π</i>

Classification of Complete Regular Minimal Surfaces in ℝ<i><sup>n</sup></i> with Total Curvature −6<i>π</i>

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...

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Bibliographic Details
Main Authors: Minghao Li, Li Ou, Shuangcai Zhang
Format: Article
Language:English
Published: MDPI AG 2022-05-01
Series:Mathematics
Subjects:
total curvature
complete minimal surfaces
orientable surfaces
Online Access:https://www.mdpi.com/2227-7390/10/11/1820
Description
Summary: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>.
ISSN:2227-7390

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