Scholarlink

<p>In any 5-dimensional closed Sasakian manifold, we prove that any minmax operation on the area among Legendrian surfaces is achieved by a continuous conformal Legendrian map from a closed Riemann surface <i>S</i> into <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N^5\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>N</mi> <mn>5</mn> </msup> </math></EquationSource> </InlineEquation> equipped with an integer multiplicity bounded in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>. Moreover this map, equipped with this multiplicity, satisfies a weak version of the Hamiltonian Minimal Equation. We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen–Wolfson conical singularities with non-zero Maslov class.</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

Area Variations Under Legendrian Constraint

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月17日

查看全文
  • Tristan Rivière

摘要

In any 5-dimensional closed Sasakian manifold, we prove that any minmax operation on the area among Legendrian surfaces is achieved by a continuous conformal Legendrian map from a closed Riemann surface S into \(N^5\) N 5 equipped with an integer multiplicity bounded in \(L^\infty \) L ∞ . Moreover this map, equipped with this multiplicity, satisfies a weak version of the Hamiltonian Minimal Equation. We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen–Wolfson conical singularities with non-zero Maslov class.