• 대한수학회보
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• 제61권2호
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• pp.433-450
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• 2024

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.