Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GEOMETRIC INEQUALITIES FOR AFFINE CONNECTIONS ON RIEMANNIAN MANIFOLDS

  • Huiting Chang (School of Mathematics and Statistics Xinyang Normal University) ;
  • Fanqi Zeng (School of Mathematics and Statistics Xinyang Normal University)
  • Received : 2023.03.08
  • Accepted : 2023.09.22
  • Published : 2024.03.31
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Abstract

Using a Reilly type integral formula due to Li and Xia [23], we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the 1-Bakry-Emery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.

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References

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