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<p>In this paper, we conduct a comparative analysis between the flow method in dealing with Minkowski problem of convex geometry (see Adv Math 205: 33–83, 2006) and gradient flow in nonlinear functional analysis (see Progress in Nonlinear Differential Equations and Their Applications 24: 453, 1996), revealing their connections. We also provide an example demonstrating how gradient flow can be used to obtain solutions for the planar <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> Minkowski problem.</p>

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The intrinsic connections between the curvature flow in Minkowski problem and gradient flow in nonlinear analysis

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Shen Ao,
  • Sun Yijing,
  • Tan Yuxin

摘要

In this paper, we conduct a comparative analysis between the flow method in dealing with Minkowski problem of convex geometry (see Adv Math 205: 33–83, 2006) and gradient flow in nonlinear functional analysis (see Progress in Nonlinear Differential Equations and Their Applications 24: 453, 1996), revealing their connections. We also provide an example demonstrating how gradient flow can be used to obtain solutions for the planar \(L_p\) L p Minkowski problem.