Scholarlink

<p>In this work we are going to establish Hölder continuity of harmonic maps from an open set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> in an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{RCD}(K,N)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>RCD</mtext> <mo stretchy="false">(</mo> <mi>K</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> space valued into a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{CAT}(\kappa )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>CAT</mtext> <mo stretchy="false">(</mo> <mi>κ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> space, with the constraint that the image of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> via the map is contained in a sufficiently small ball in the target. Building on top of this regularity and assuming a local Lipschitz regularity of the map, we establish a weak version of the Bochner-Eells-Sampson inequality in such a non-smooth setting. Finally we study the boundary regularity of such maps.</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

Comments on the Regularity of Harmonic Maps Between Singular Spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月11日

查看全文
  • Luca Gennaioli,
  • Nicola Gigli,
  • Hui-Chun Zhang,
  • Xi-Ping Zhu

摘要

In this work we are going to establish Hölder continuity of harmonic maps from an open set \(\Omega \) Ω in an \(\textrm{RCD}(K,N)\) RCD ( K , N ) space valued into a \(\textrm{CAT}(\kappa )\) CAT ( κ ) space, with the constraint that the image of \(\Omega \) Ω via the map is contained in a sufficiently small ball in the target. Building on top of this regularity and assuming a local Lipschitz regularity of the map, we establish a weak version of the Bochner-Eells-Sampson inequality in such a non-smooth setting. Finally we study the boundary regularity of such maps.