Fattening on two dimensions obtained with a nonsymmetric anisotropy: Numerical simulations.
Paolini, M. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Paolini, M. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Mayer, Uwe F. (2001)
Experimental Mathematics
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Nobumitsu Nakauchi (1993)
Manuscripta mathematica
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Hitoshi Imai, Naoyuki Ishimura, TaKeo Ushijima (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Giuseppe Pipoli (2017)
Complex Manifolds
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In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.
Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The existence of a singular curve in is proven, whose curvature can be extended to an function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.
R. H. Nochetto, M. Paolini, C. Verdi (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Xu-Jia Wang (2014)
Journal of the European Mathematical Society
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The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
Ronaldo García, Jorge Sotomayor (2001)
Publicacions Matemàtiques
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In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [GS2], whose lines produce the extremal for the immersion, the pair of foliations by lines of...