Lectures on Finsler Geometry

By Zhongmin Shen. 2001

704 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7a8b461caf90c46ed5049d3ddfaa2f298ad06437

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In Astronomy and Astrophysics

Citations in the corpus

Landsberg Curvature, S-Curvature and Riemann Curvature (2004, background): “By the calculus of variation, one can show that geodesics are characterized by a system of 2nd order ordinary differential equations (see e.g. [Shen 2001a], [Shen 2001b]).”
Finsler interpolation inequalities (2009, background): “1, see also [Sh2] for applications) is usable, whereas we also give a new, sharper comparison theorem (Theorem 7.”
Finsler manifolds with nonpositive flag curvature and constant S-curvature (2003, background): “S = S(x, y) is a scalar function on TMo which is called the S-curvature [16][17].”
The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces (2012, neutral): “[She01], [OS09]), finite dimensional Alexandrov spaces (cf.”
Nonreversible Finsler Metrics of Positive Flag Curvature (2004, methodology): “The exponential map expp : TpM → M is C∞-smooth on TpM \ {0} and C1-smooth on TpM [Shen 2001a, § 11.1].”
Finsler Conformal Lichnerowicz-Obata conjecture (2008, methodology): “As an interesting and much more involved problem in Finsler geometry related to transformation groups we would like to suggest to generalize the projective Lichnerowicz-Obata conjecture for Finsler metrics, see [Ma1, Ma2] for the proof of the Riemannian version, see also [ Sh ].”
Uniform convexity and smoothness, and their applications in Finsler geometry (2009, methodology): “as in [Sh2] and [Sh3] might be more natural in some situations, we prefer (2.”
RANDERS METRICS OF SCALAR FLAG CURVATURE (2009, methodology): “The S-curvature S(x,y) measures the average rate of changes of (TxM,Fx )i n the direction y 2 TxM . An important property is that S = 0 for Berwald spaces [11][ 12 ].”
An optimal anisotropic Poincaré inequality for convex domains (2011, methodology): “natural) generalization to Finsler manifolds. In fact, Rn with F can be viewed as a special Finsler manifold. On a general Finsler manifold, there is a generalized Finsler-Laplacian, see for instance [7, 14, 18]. A Lichnerowicz type result for the ﬁrst eigenvalue of this Laplacian was obtained in [1”
Multiple closed geodesics on bumpy Finsler n-spheres (2007, methodology): “For the definition of closed geodesics on a Finsler manifold, we refer readers to [3] and [28].”
A class of Finsler metrics with isotropic S-curvature (2009, background): “1 Let F = α+β be the family of Randers metrics on S(3) constructed in [3] (see also [16]).”
Heat flow on Finsler manifolds (2008, methodology): “For further reading and more details, we refer to [BCS] and [Sh3].”
Displacement convexity of generalized relative entropies (2010, methodology): “We refer to [BCS], [Sh] for the basics of Finsler geometry, and to [Oh2], [OS1], [Oh3] for the details omitted in the following discussion.”
Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties (2008, background): “In Finsler geometry, there are several geometric quantities: the Riemann curvature (the flag curvature), the distortion, the (mean) Cartan curvature, the S-curvature, the (mean) Landsberg curvature and the (mean) Berwald curvature, etc. (Cf. [7] [8]).”
Stability of closed geodesics on Finsler 2-spheres (2008, neutral): “[28].”
A Finsler geodesic spray paradigm for wildfire spread modelling (2016, methodology): “Finsler metrics By classical definition, see [10] and [11], a Finsler metric on a domain U is a smooth family of Minkowski norms on the tangent planes, i.”