Book Review: Space mappings with bounded distortion
نویسندگان
چکیده
منابع مشابه
Mappings of Bounded Mean Distortion and Cohomology
T 2 are the only closed Riemann surfaces admitting nonconstant conformal mappings from the complex plane. The same rigidity is present in higher dimensions; closed manifolds admitting conformal mappings from Rn are quotients of Sn and Tn, see e.g. [2, Prop. 1.4]. However, if distortion is allowed, simple examples show that the spaces Sk1 × Sk2 × · · · × Skl (k1 + · · ·+ kl = n) receive nonconst...
متن کاملMappings of Bounded Distortion Between Complex Manifolds
We obtain Liouville type theorems for holomorphic mappings with bounded s-distortion between Cn and positively curved Kähler manifolds.
متن کاملThe Limit of Mappings with Finite Distortion
We show here that the limit mapping f of a weakly convergent sequence of mappings fν with finite distortion also has finite distortion and give several dimension free estimates for the dilatation of f . Our arguments are based on the weak continuity of the Jacobian determinants and the concept of polyconvexity.
متن کاملBounded-Distortion Metric Learning
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents bounded-distortion metric learning (BDML), a new metric learning framework which amounts to finding an optimal Mahalan...
متن کاملExtremal Mappings of Finite Distortion
The theory of mappings of nite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting. There one nds concrete applications in materials science, particularly non-linear elasticity and critical phase phenomena, and the calculus of variations. In this paper we re ne and extend these connections...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1991
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1991-16051-9