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Relative K-stability of extremal metrics

Jacopo Stoppa, Gábor Székelyhidi (2011)

Journal of the European Mathematical Society

We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.

Relaxed hyperelastic curves

Ahmet Yücesan, Gözde Özkan, Yasemín Yay (2011)

Annales Polonici Mathematici

We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.

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