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# Classification of conformal metrics on $R/FORMULA> with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions AUTHOR(S) Lei Zhang PUB. DATE April 2003 SOURCE Calculus of Variations & Partial Differential Equations;Apr2003, Vol. 16 Issue 4, p405 SOURCE TYPE Academic Journal DOC. TYPE Article ABSTRACT No abstract available. ACCESSION # 11998756 ## Related Articles • Variational properties of the Gaussï¿½Bonnet curvatures. Labbi, M.-L. // Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p175 The Gaussï¿½Bonnet curvature of order 2 k is a generalization to higher dimensions of the Gaussï¿½Bonnet integrand in dimension 2 k, as the scalar curvature generalizes the two dimensional Gaussï¿½Bonnet integrand. In this paper, we evaluate the first variation of the integrals of these... • WEIERSTRASS REPRESENTATION FOR SURFACES WITH PRESCRIBED NORMAL GAUSS MAP AND GAUSS CURVATURE IN H3. Shuguo, Shi // Chinese Annals of Mathematics;Oct2004, Vol. 25 Issue 4, p567 The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss... • The geometric Neumann problem for the Liouville equation. Gálvez, José; Jiménez, Asun; Mira, Pablo // Calculus of Variations & Partial Differential Equations;Jul2012, Vol. 44 Issue 3/4, p577 Let Î© denote the upper half-plane $${\mathbb{R}_+^2}$$ or the upper half-disk $${D_{\varepsilon}^+\subset \mathbb{R}_+^2}$$ of center 0 and radius $${\varepsilon}$$. In this paper we classify the solutions $${v\in\;C^2(\overline{\Omega}\setminus\{0\})}$$ to the Neumann problemwhere $${K, c_1,... • TRANSLATION SURFACES WITH CONSTANT MEAN CURVATURE IN 3-DIMENSIONAL SPACES. Huili Liu // Journal of Geometry;Mar1999, Vol. 64 Issue 1/2, p141 Focuses on the classification of the translation surfaces with constant mean curvature. Determination of Gauss curvature in three-dimensional Euclidean and Minkowski space; Problem in constructing the constant mean curvature; Analysis of mean curvature hypersurfaces in arbitrary spacetime. • Local pointwise estimates for solutions of the Ïƒ2 curvature equation on 4-manifolds. Han, Zheng-Chao // IMRN: International Mathematics Research Notices;2004, Vol. 2004 Issue 79, p4269 The study of the kth elementary symmetric function of the Weyl-Schouten curvature tensor of a Riemannian metric, the so called Ïƒk curvature, has produced many fruitful results in conformal geometry in recent years, especially when the dimension of the underlying manifold is 3 or 4. In these... • A note of Sasakian metrics with constant scalar curvature. Xi Zhang // Journal of Mathematical Physics;Oct2009, Vol. 50 Issue 10, p103505 In this paper, we consider compact Sasakian manifolds with constant scalar curvature. Under some positive curvature assumption, we prove that such Sasakian metrics must be Î·-Einstein metrics. • Minimizers of a weighted maximum of the Gauss curvature. Moser, Roger; Schwetlick, Hartmut // Annals of Global Analysis & Geometry;Feb2012, Vol. 41 Issue 2, p199 On a Riemann surface$${\overline{\Sigma}}$$with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let Îº be a smooth, positive function on$${\overline{\Sigma}}$\$. If K denotes the Gauss curvature, then the L-norm of K/ Îº gives rise to a functional on...

• Affine Translation Surfaces with Constant Gaussian Curvature. Yu Fu; Zhong-Hua Hou // Kyungpook Mathematical Journal;Jun2010, Vol. 50 Issue 2, p337

We study affine translation surfaces in â„3 and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• The Moyal sphere. Eckstein, Michał; Sitarz, Andrzej; Wulkenhaar, Raimar // Journal of Mathematical Physics;2016, Vol. 57 Issue 11, p1

We construct a family of constant curvature metrics on the Moyal plane and compute the Gauss-Bonnet term for each of them. They arise from the conformal rescaling of the metric in the orthonormal frame approach. We find a particular solution, which corresponds to the Fubini-Study metric and...

• TWO CLASSES OF CONFORMALLY FLAT CONTACT METRIC 3-MANIFOLDS. Gouli-Andreou, Florence; Xenos, Philippos J. // Journal of Geometry;Mar1999, Vol. 64 Issue 1/2, p80

Focuses on the classification of three-dimensional conformally flat contact metric manifolds. Description of the contact manifold of constant curvature; Concept of Sasakian manifolds; Application of D-homothetic deformation on a contact metric manifold.

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