Bauer, Matthias; Kuwert, Ernst Existence of minimizing Willmore surfaces of prescribed genus. (English) Zbl 1029.53073 Int. Math. Res. Not. 2003, No. 10, 553-576 (2003). The authors consider an immersed surface \(f:\Sigma \to\mathbb{R}^n\), the Willmore integral \({\mathcal W}(f)= \int_\Sigma|{\mathcal H}|^2 d\mu\), \(({\mathcal H}=\) the mean curvature vector and \(\mu=\) the induced area measure) and \(\beta_{\mathfrak p}=\inf \{{\mathcal W}(f); f\in{\mathcal S}_{\mathfrak p}\}\) \(({\mathcal S}_{\mathfrak p}=\) the class of immersions \(f\), where \(\Sigma\) is an orientable, closed surface with genus \((\Sigma)={\mathfrak p})\). They prove (Theorem 1.2): For any \({\mathfrak p}\in \mathbb{N}_0\) the infimum \(\beta_{\mathfrak p}\) is attained by an oriented, closed Willmore surface of genus \({\mathfrak p}\). Reviewer: A.Neagu (Iaşi) Cited in 58 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C43 Differential geometric aspects of harmonic maps 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:Willmore integral; mean curvature vector; Willmore energy; closed immersed surface PDFBibTeX XMLCite \textit{M. Bauer} and \textit{E. Kuwert}, Int. Math. Res. Not. 2003, No. 10, 553--576 (2003; Zbl 1029.53073) Full Text: DOI