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等周型不等式及其稳定性
The Isoperimetric Type Inequality and Its Stability

DOI: 10.12677/pm.2025.155179, PP. 298-310

Keywords: 等周不等式，曲率中心轨迹，稳定性，Bonnesen型不等式
Isoperimetric Inequality, Locus of Curvature Centers, Stability, Bonnesen-Type Inequalities

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Abstract:

本文建立了一个新的几何量——沿外法线向量的曲率轨迹，探讨了其几何意义及其与曲率中心轨迹的关系。并利用新的几何量建立了一组参数不等式： α ∫ γ κ 2 ds+β ∫ 0 2π ρ 2 ( θ )dθ+λ ∫ 0 2π ρ β 2 ( θ )dθ+δ L 2 +σA +？ω| A ？ |+μ| A ^ |+ν ∫ 0 2π ρ β ^ 2 ( θ )dθ+ζ ( ρ M ？ ρ m

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