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<p>In this paper, we obtain several classification results of 2-dimensional complete Lagrangian translators and lagrangian self-expanders with constant squared norm <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="229_2025_1633_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(|\vec {H}|^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <mover accent="true"> <mi>H</mi> <mo stretchy="false">→</mo> </mover> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> of the mean curvature vector in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="229_2025_1633_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> by using a new Omori–Yau type maximum principle which was proved by Chen and Qiu (Adv Math 294:517–531, 2016). The same idea is also used to give a similar result of Lagrangian <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="229_2025_1633_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation>-translators in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="229_2025_1633_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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Classification of Lagrangian translators and Lagrangian self-expanders in \(\mathbb {C}^{2}\)

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • Zhi Li,
  • Guoxin Wei

摘要

In this paper, we obtain several classification results of 2-dimensional complete Lagrangian translators and lagrangian self-expanders with constant squared norm \(|\vec {H}|^{2}\) | H → | 2 of the mean curvature vector in \(\mathbb {C}^{2}\) C 2 by using a new Omori–Yau type maximum principle which was proved by Chen and Qiu (Adv Math 294:517–531, 2016). The same idea is also used to give a similar result of Lagrangian \(\xi \) ξ -translators in \(\mathbb {C}^{2}\) C 2 .