Scholarlink

<p>In this paper, by using a special Euler–Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in the Lorentz–Minkowski 3-space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {E}_1^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="double-struck">E</mi> <mn>1</mn> <mn>3</mn> </msubsup> </math></EquationSource> </InlineEquation>, namely Scherk-type zero mean curvature surfaces, can be expressed as an infinite superposition of dilated helicoids. Further, we also obtain different finite decompositions for these surfaces. We end this paper with an application of these decompositions to formulate maximal codimension 2 surfaces into finite and infinite “sums” of weakly untrapped and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-surfaces in the Lorentz–Minkowski 4-space.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Decompositions of Scherk-type zero mean curvature surfaces

  • 期刊论文

  • 发表日期：

    2025年11月14日

查看全文
  • Subham Paul,
  • Priyank Vasu,
  • Siddharth Panigrahi,
  • Rahul Kumar Singh

摘要

In this paper, by using a special Euler–Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in the Lorentz–Minkowski 3-space \(\mathbb {E}_1^3\) E 1 3 , namely Scherk-type zero mean curvature surfaces, can be expressed as an infinite superposition of dilated helicoids. Further, we also obtain different finite decompositions for these surfaces. We end this paper with an application of these decompositions to formulate maximal codimension 2 surfaces into finite and infinite “sums” of weakly untrapped and \(*\) ∗ -surfaces in the Lorentz–Minkowski 4-space.