Showing items with similar title or keywords.

• On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups 

  Fässler, Katrin; Le Donne, Enrico (Springer, 2021)

  This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give ...

• Plenty of big projections imply big pieces of Lipschitz graphs 

  Orponen, Tuomas (Springer, 2021)

  I prove that closed n-regular sets E⊂Rd with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

• Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups 

  Di Donato, Daniela; Fässler, Katrin (Springer, 2022)

  This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group Hn, n∈N. For 1⩽k⩽n, we show that every intrinsic L-Lipschitz graph over a subset ...

• A remark on two notions of flatness for sets in the Euclidean space 

  Violo, Ivan Yuri (Walter de Gruyter GmbH, 2022)

  In this note we compare two ways of measuring the n-dimensional “flatness” of a set S⊂RdS⊂ℝd , where n∈Nn∈ℕ and d>nd>n . The first is to consider the classical Reifenberg-flat numbers α(x,r)α⁢(x,r) ( x∈Sx∈S , r>0r>0 ), ...

• Geometric Inverse Problems : With Emphasis on Two Dimensions 

  Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther (Cambridge University Press, 2023)

  This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered ...