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<p>The nonlocal <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\text {r-}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>r-</mtext> </math></EquationSource> </InlineEquation>perimeter is a significant geometric functional that quantifies the interaction between the boundary of a set and its surroundings within a given radius <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( r \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation>. In this paper, we introduce two nonlocal perimeter measures associated with the nonlocal <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text {r-}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>r-</mtext> </math></EquationSource> </InlineEquation>perimeter and provide a detailed study of their properties. Additionally, we pose and solve the nonlocal perimeter Minkowski problem and the nonlocal perimeter log-Minkowski problem for characterizing these two measures.</p>

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On the nonlocal r-perimeter Minkowski problem

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Lu Zhang

摘要

The nonlocal \(\text {r-}\) r- perimeter is a significant geometric functional that quantifies the interaction between the boundary of a set and its surroundings within a given radius \( r \) r . In this paper, we introduce two nonlocal perimeter measures associated with the nonlocal \(\text {r-}\) r- perimeter and provide a detailed study of their properties. Additionally, we pose and solve the nonlocal perimeter Minkowski problem and the nonlocal perimeter log-Minkowski problem for characterizing these two measures.