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A Class of Prescribed Weingarten Curvature Equations for Locally Convex Hypersurfaces with Boundary in \(\mathbb {R}^{n+1}\)

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Abstract

In this paper, we consider a class of prescribed Weingarten curvature equations for strictly locally convex hypersurfaces with boundary in \(\mathbb {R}^{n+1}\). Under some sufficient conditions, we obtain an existence result using a two-step continuity process based on the a priori estimates for solutions to prescribed Weingarten curvature equations.

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, People’s Republic of China

    Yan He, Qiang Tu & Ni Xiang

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  1. Yan He
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  2. Qiang Tu
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  3. Ni Xiang
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Correspondence to Qiang Tu.

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This research was supported by funds from the National Natural Science Foundation of China Nos. 11971157, 12101206.

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He, Y., Tu, Q. & Xiang, N. A Class of Prescribed Weingarten Curvature Equations for Locally Convex Hypersurfaces with Boundary in \(\mathbb {R}^{n+1}\). J Geom Anal 34, 48 (2024). https://doi.org/10.1007/s12220-023-01496-3

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