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Narrow-linewidth lasing and soliton Kerr microcombs with ordinary laser diodes
Nature Photonics, 2018Nikolay G Pavlov +2 more
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Resonant excitation and all-optical switching of femtosecond soliton molecules
Nature Photonics, 2019Felix Kurtz, Claus Ropers, Georg Herink
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ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2010 We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties.
Alberto +4 more
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Uniqueness of Kähler-Ricci solitons [PDF]
Acta Mathematica, 2000 Let \(X\) be a holomorphic vector field on a compact Kähler manifold \((M,\omega)\). Then \(\omega\) is a Kähler-Ricci soliton with respect to \(X\) if \(\text{Ric} (\omega)-\omega=L_X\omega\) where \(\text{Ric} (\omega)\) is the Ricci form and \(L_X\) is the Lie derivative with respect to \(X\).
Gang Tian, Xiaohua Zhu
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Stability and instability of Ricci solitons [PDF]
Calculus of Variations and Partial Differential Equations, 2014 We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $(M,g)$ is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time ...
Kroencke, Klaus
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Homogeneous Ricci solitons [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2011 Abstract In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat, it is necessarily simply-connected and diffeomorphic to ℝ n
R Lafuente, Jorge Lauret
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Characterizations of Trivial Ricci Solitons [PDF]
Advances in Mathematical Physics, 2020 Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton.
Sharief Deshmukh +2 more
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On homogeneous Ricci solitons [PDF]
The Quarterly Journal of Mathematics, 2012 We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e.
R Lafuente, Jorge Lauret
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