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Giuseppe Tinaglia’s Home Page |
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research interest is geometric
analysis with emphasis currently on the theory of minimal and constant mean
curvature surfaces. Minimal surfaces are defined as surfaces which are critical points for the area functional. The mean curvature of a minimal surface, the average of the two principal curvatures, is identically zero. Surfaces which are critical points for the area functional under a volume constraint are instead called constant mean curvature (CMC) surfaces and in fact the average of the two principal curvatures is constant. Not only are there plenty of mathematical examples for both of these surfaces (for instance planes, helicoids and catenoids are minimal surfaces while spheres, cylinders and Delaunay surfaces are non zero CMC surfaces), but they can easily be realized and observed in the real world. In nature, the shape of a soap film approximates with great accuracy that of a minimal surface while soap bubbles provide the analogous approximation for CMC surfaces. In other words, a soap bubble is the least-area surface that encloses the fixed volume inside. |
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Papers
The available papers/preprints are posted on the arXiv. For a copy please clck here. If you do not have access to the arXiv, please send me an email at giuseppetinaglia at gmail dot com G. Tinaglia, Local behavior of embedded constant mean curvature disks, Seminari di Geometria 2001-2004, Universita' di Bologna: 73-80. B. Dean and G. Tinaglia, A generalization of Rado’s theorem for almost graphical boundaries, Math. Zeit., 251:849–858, 2005, arXiv:0502551 G. Tinaglia, Multi-valued graphs in embedded constant mean curvature disks, Trans. Amer. Math. Soc., 359:143–164, 2007, arXiv:0409184 G. Tinaglia, Structure theorems for embedded disks with mean curvature bounded in L^P, Comm. Anal. Geom. 16 (2008), no. 4, 819–836, arXiv:0712.0409 G. Tinaglia, Curvature bounds for minimal surfaces with total boundary curvature less than 4\pi, to appear in Proceedings of the American Mathematical Society, arXiv:0712.1500 W. H. Meeks III and G. Tinaglia, The Dynamics Theorem for CMC surfaces in R^3, to appear in Journal of Differential Geometry, arXiv:0805.1427 W. H. Meeks III and G. Tinaglia, The rigidity of constant mean curvature surfaces, arXiv:0801.3409v1 B. Smyth and G. Tinaglia, The number of constant mean curvature isometric immersions of a surface, arXiv:0801.3409 Work in progress W. H. Meeks III and G. Tinaglia, Curvature estimates for constant mean curvature surfaces. W. H. Meeks III and G. Tinaglia, One-sided curvature estimates for H-disks. W. H. Meeks III and G. Tinaglia, Chord-arc bounds for H-disks. W. H. Meeks III and G. Tinaglia, Properness results for constant mean curvature surfaces. W. H. Meeks III and G. Tinaglia, CMC surfaces in locally homogeneous three-manifolds. W. H. Meeks III and G. Tinaglia, The CMC dynamics theorem in homogeneous n-manifolds. B. Nelli and G. Tinaglia, Vertical annuli of constant mean curvature in H^2xR. B. Smyth and G. Tinaglia, The associate immersions of a constant mean curvature surface. |