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<p>We generalize Schulz’s estimate to general three-dimensional Riemannian manifolds. As an application, we provide a unified approach to the Weyl problem in space forms. A Minkowski-type formula is applied to obtain an upper bound for total mean curvature. Combined with Lu’s estimates, we improve Guan-Lu’s existence result on Weyl embedding problem in warped product spaces to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2041_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(g\in C^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>∈</mo> <msup> <mi>C</mi> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The Heinz-Lewy System and The Weyl Embedding Problem in Warped Product Spaces

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Zhuo Chen

摘要

We generalize Schulz’s estimate to general three-dimensional Riemannian manifolds. As an application, we provide a unified approach to the Weyl problem in space forms. A Minkowski-type formula is applied to obtain an upper bound for total mean curvature. Combined with Lu’s estimates, we improve Guan-Lu’s existence result on Weyl embedding problem in warped product spaces to \(g\in C^{3}\) g ∈ C 3 .