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Surfaces with non-zero normal curvature tensor

Antonio Carlos Asperti, Dirk Ferus, Lucio Rodriguez (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Studiamo la topologia differenziale e la geometria delle superfici compatte con curvatura normale non-nulla in spazio della curvatura costante.

Surfaces with prescribed Weingarten operator

Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)

Banach Center Publications

We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.

Symplectic critical surfaces in Kähler surfaces

Xiaoli Han, Jiayu Li (2010)

Journal of the European Mathematical Society

Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = Σ 1 cos α d μ in the class of symplectic surfaces. It is cos 3 α H = ( J ( J cos α ) ) , where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M , which is an elliptic equation. We call such a surface a symplectic critical surface. We show that, if M is a Kähler-Einstein surface with nonnegative...

The area preserving curve shortening flow with Neumann free boundary conditions

Elena Mäder-Baumdicker (2015)

Geometric Flows

We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.

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