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arXiv · 2407.18776

Prescribing almost constant curvatures on manifolds with boundary

Luca Battaglia·Yixing Pu
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Abstract

In this paper, we investigate a boundary case of the classical prescribed curvature problem. We focus on prescribing the scalar curvature function K and the boundary mean curvature H on the standard ball. Our analysis extendes previous studies by considering the scenario where the curvatures K and H are close to constants. Using a perturbative approach and leveraging the ansatz introduced by Han and Li, we establish new existence results for the conformal metric when the prescribed curvatures are near constants

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Luca Battaglia, Yixing Pu. 2024-07-26. Prescribing almost constant curvatures on manifolds with boundary. https://arxiv.org/abs/2407.18776

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