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Closed Legendre geodesics in Sasaki manifolds.

Smoczyk, Knut (2003)

The New York Journal of Mathematics [electronic only]

Computational study of the Willmore flow on graphs

Oberhuber, Tomáš (2007)

Proceedings of Equadiff 11

Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds

Tamalika Dutta, Nirabhra Basu, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $α$ -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton is $η$ -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian $α$ -Sasakian...

Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

Francesca Da Lio, N. Forcadel, Régis Monneau (2008)

Journal of the European Mathematical Society

We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.

Convexity estimates for flows by powers of the mean curvature

Felix Schulze (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the evolution of a closed, convex hypersurface in $ℝ^{n + 1}$ in direction of its normal vector, where the speed equals a power $k \geq 1$ of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to $1$ , depending only on $k$ and $n$ , then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.

Curvature flows on surfaces

Michael Struwe (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.

Curve shortening flow and the Banchoff-Pohl inequality on surfaces of nonpositive curvature.

Süssmann, Bernd (1999)

Beiträge zur Algebra und Geometrie