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<p>For a closed connected manifold immersed in a complete noncompact manifold with asymptotically nonnegative sectional curvature and no vanishing asymptotic volume ratio, we estimate its intrinsic diameter in terms of its mean curvature and certain sectional curvature quantity integrals. For a compact surface with boundary immersed in such an ambient manifold, we can estimate its intrinsic diameter in terms of its mean curvature and certain sectional curvature quantity integrals, and the length of its boundary. These results are regarded as some supplements of previous results of Topping, Wu-Zheng, Paeng and the third author.</p>

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Diameter Bounds for Submanifolds in Manifolds with Asymptotically Nonnegative Curvature

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Leyi Liu,
  • Shengqiang Tai,
  • Jia-Yong Wu

摘要

For a closed connected manifold immersed in a complete noncompact manifold with asymptotically nonnegative sectional curvature and no vanishing asymptotic volume ratio, we estimate its intrinsic diameter in terms of its mean curvature and certain sectional curvature quantity integrals. For a compact surface with boundary immersed in such an ambient manifold, we can estimate its intrinsic diameter in terms of its mean curvature and certain sectional curvature quantity integrals, and the length of its boundary. These results are regarded as some supplements of previous results of Topping, Wu-Zheng, Paeng and the third author.