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<p>We compute the second inner variation of the Abelian Yang–Mills–Higgs and Ginzburg–Landau energies. Given a sequence of critical points with energy measures converging to a codimension 2 minimal submanifold, we use the second inner variation formula to bound the Morse index of the submanifold by the index of the critical points. The key tools are the convergence of the energy measures and the stress-energy tensors of solutions to Abelian Yang–Mills–Higgs and Ginzburg–Landau equations. We further apply this methodology to control the limiting varifold of a sequence of stable Allen–Cahn solutions with Neumann condition on the boundary.</p>

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Second Inner Variations, Stress-Energy Tensors, and Index of Limiting Varifolds

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Jared Marx-Kuo

摘要

We compute the second inner variation of the Abelian Yang–Mills–Higgs and Ginzburg–Landau energies. Given a sequence of critical points with energy measures converging to a codimension 2 minimal submanifold, we use the second inner variation formula to bound the Morse index of the submanifold by the index of the critical points. The key tools are the convergence of the energy measures and the stress-energy tensors of solutions to Abelian Yang–Mills–Higgs and Ginzburg–Landau equations. We further apply this methodology to control the limiting varifold of a sequence of stable Allen–Cahn solutions with Neumann condition on the boundary.