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It is well-known that a stable surface is area-minimizing relative to nearby surfaces with the same boundary. In variational terms, minimal surfaces are critical points of the area functional for compactly supported normal variations. In this setting, a minimal surface is stable if the second derivative of the area functional is nonnegative for such normal variations. On the other hand, when the second variation is negative for some deformation, there are nearby surfaces of smaller area, and the surface is called unstable.

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\(L_{\varphi }\) -Stability of Zero \(\varphi \) -Mean Curvature Hypersurfaces

  • 章节

  • 发表日期：

    2025年

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  • Henrique Fernandes de Lima,
  • Giovanni Molica Bisci,
  • Marco Antonio Lázaro Velásquez

摘要

It is well-known that a stable surface is area-minimizing relative to nearby surfaces with the same boundary. In variational terms, minimal surfaces are critical points of the area functional for compactly supported normal variations. In this setting, a minimal surface is stable if the second derivative of the area functional is nonnegative for such normal variations. On the other hand, when the second variation is negative for some deformation, there are nearby surfaces of smaller area, and the surface is called unstable.