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<p>We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Langford and Scheuer (Commun Partial Differ Equ 46(6):1005–1016, 2021). To the best of our knowledge, this is the first general concavity principle established on spaces with non-constant sectional curvature.</p>

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Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月10日

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  • Shrey Aryan,
  • Michael B. Law

摘要

We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Langford and Scheuer (Commun Partial Differ Equ 46(6):1005–1016, 2021). To the best of our knowledge, this is the first general concavity principle established on spaces with non-constant sectional curvature.