G. David and S. Semmes Fractured fractals and broken dreams – self-similar geometry through metric and measure (Oxford Lecture Series in Mathematics and its Applications Vol. 7, Clarendon Press, Oxford, 1997), ix + 212pp., 0 19 850166 8, (hardback) £35. [PDF]
Proceedings of the Edinburgh Mathematical Society, 1999 K. J. Falconer
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Projective Metric Geometry and Clifford Algebras [PDF]
Results in Mathematics, 2021 Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group.
H. Havlicek
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Stress and Geometry for Isotropic Singularities. [PDF]
Physical Review Letters, 2023 We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general relativistic stress ...
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Hessian metric via transport information geometry [PDF]
Journal of Mathematics and Physics, 2020 We propose to study the Hessian metric of given functional in the space of probability space embedded with $L^2$--Wasserstein (optimal transport) metric.
Wuchen Li
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Design of 3D Metric Geometry Study and Research Activities within a BIM Framework
Mathematics, 2022 This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences.
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AIMS Mathematics, 2023 We introduce an $ \mathcal{M-} $class function in an $ \mathcal{S-} $metric space which is a viable, productive, and powerful technique for finding the existence of a fixed point and fixed circle.
M. Joshi, A. Tomar, T. Abdeljawad
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Geometry, analysis, and morphogenesis: Problems and prospects [PDF]
Bulletin of the American Mathematical Society, 2021 The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics, and mathematics.
M. Lewicka, L. Mahadevan
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Moufang Patterns and Geometry of Information [PDF]
Pure and Applied Mathematics Quarterly, 2021 Technology of data collection and information transmission is based on various mathematical models of encoding. The words"Geometry of information"refer to such models, whereas the words"Moufang patterns"refer to various sophisticated symmetries appearing
N. Combe, Y. Manin, M. Marcolli
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COARSE AND FINE GEOMETRY OF THE THURSTON METRIC [PDF]
Forum of Mathematics, Sigma, 2016 We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type; however, we focus particular ...
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Geometric interpretation and visualization of particular geometric concepts at metric spaces study
Journal of Physics: Conference Series, 2022 The paper considers the issues of studying method of geometric properties of metric spaces. These questions arise when students learn the basic concepts of the metric spaces theory.
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