Differential structure on partial isometries over Grassmannian constructed.
problem No specific problem stated; abstract focuses on method and result.
method Construction of differential structure on partial isometries over restricted Grassmannian.
result Set of partial isometries over restricted Grassmannian becomes a Banach Lie groupoid.
For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also determine a gap in the possible dimensions of the isometry groups and show that…
Characterizes self-isometries of Riemannian metrics on compact manifolds.
problem Understanding isometries of Riemannian metrics.
method Characterization of self-isometries and proof of isometry conditions.
result Two Riemannian metric spaces are isometric if and only if their manifolds are diffeomorphic.
We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains an index two subgroup of isometries that extend.
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
Given a metric space X, one defines its Wasserstein space W2(X) as a set of sufficiently decaying probability measures on X endowed with a metric defined from optimal transportation. In this article, we continue the geometric study of W2(X) when X is a simply connected, nonpositively curved metric spaces by considering…
The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.
problem Understanding quasi-isometry in almost contact metric manifolds.
method Definition and study of quasi-isometry for almost contact metric manifolds.
result Established a relation between scalar curvature and quasi-isometric constants.
The paper explores additional structures on Morse boundaries to distinguish hyperbolic spaces up to quasi-isometry.
problem Distinguishing hyperbolic spaces up to quasi-isometry using additional structures on Morse boundaries.
method Investigates additional structures on Morse boundaries and proves conditions for a homeomorphism to be induced by a quasi-isometry.
result A homeomorphism between Morse boundaries of hyperbolic spaces is induced by a quasi-isometry if and only if it is bihölder, quasi-symmetric, or strongly quasi-conformal.
We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the secon…
The study classifies Heintze groups up to isometry and quasi-isometry in low dimensions.
problem Classifying Heintze groups up to isometry and quasi-isometry in low dimensions.
method Analyzing quasi-isometries and isometries of Heintze groups, applying existing tools to groups of dimension 4 and 5.
result Complete classification of simply connected solvable groups in dimension 4 and groups of polynomial growth in dimension 5 up to isometry.
It is of interest to characterize algebraically the dynamical types of isometries of the complex and quaternionic hyperbolic planes. In the complex case, such a characterization is known from the work of Giraud-Goldman. In this paper, we offer an algebraic characterization of the isometries of the two-dimensional quate…
Mathematical study of instanton corrected q-map spaces and their isometries.
problem Understanding the isometries of instanton corrected q-map spaces.
method Study of isometries of instanton corrected q-map spaces associated to PSR manifolds.
result Explicit example of instanton corrected q-map space with full SL(2,Z) acting by isometries.
Algorithm for Teichmüller isometries induced by periodic mapping classes
problem Determining isometries in Teichmüller space induced by periodic mapping classes
method Algorithm using Fenchel-Nielsen coordinates
result Description of isometry induced by periodic mapping class of order 4g+2 Measure-scaling quasi-isometries on graphs have specific scaling groups.
problem Understanding the scaling groups of graphs under quasi-isometries.
method Analyzing measure-scaling quasi-isometries on graphs and their properties.
result The scaling group of a graph is invariant under measure-scaling quasi-isometries.
The geometry of conjugation is mapped within Euclidean isometry groups.
problem Understanding conjugacy classes and their transformations in Euclidean groups.
method Geometric description of conjugacy classes and sets of conjugating elements based on linearizations.
result The conjugacy classes and sets of conjugating elements are described by the move-set and fix-set of linearizations.
We study the varieties of invariant totally geodesic submanifolds of isometries of the spherical, Euclidean and hyperbolic spaces in each finite dimension. We show that the dimensions of the connected components of these varieties determine the orbit type (or the z-class) of the isometry. For this purpose, we introduce…
Lifts isometries in orbit spaces for compact groups.
problem Isometries in orbit spaces of compact groups.
method Equivariant isometry of original Euclidean space.
result Simple formula for connected component of isometry group.
Study quasi-isometry invariants of square complexes and their applications.
problem Classifying quasi-isometry types of 2D right-angled Artin groups and graph 2-braid groups.
method Define and analyze intersection complexes for universal covers of weakly special square complexes.
result Discover new quasi-isometric relationships between graph 2-braid groups and right-angled Artin groups.
Sharp stability of isometries on Heisenberg group proven.
problem Quantitative stability of isometries on the Heisenberg group.
method Proving quasi-isometries close to isometries with specific closeness orders.
result Quasi-isometries of Heisenberg group are close to isometries with specific closeness orders.
Study reveals structure of isometry group for specific manifolds.
problem Understanding the isometry group of non-compact, homogeneous manifolds.
method Analyzes non-compact, homogeneous manifolds with immortal Ricci flows.
result Establishes structure result for isometry group.
Study on holomorphic isometries between complex domains, revealing geometric properties.
problem Characterizing holomorphic isometries between bounded symmetric domains.
method Analyzing holomorphic isometries between complex unit ball and other bounded symmetric domains, using classical results for complex-analytic subvarieties of Stein manifolds.
result Images of holomorphic isometries have specific geometric properties, including intersections with affine-linear subspaces.
We prove that the identity component of the holomorphic isometry group of a Sasaki-Einstein metric is the identity component of a maximal compact subgroup of its automorphism group.
Study finds all isometries for specific Lie groups.
problem Identifying isometry groups in nonunimodular Lie groups.
method Examined left-invariant Riemannian metrics on Lie groups of dimension four.
result Determined full group of isometries for each metric.
Explicit isometry groups found for nearly Kähler manifolds.
problem Understanding the symmetries of nearly Kähler manifolds.
method Alternative, less algebraic approach to find isometry groups.
result Explicit expression for isometry groups of six-dimensional nearly Kähler manifolds.
A special group of transformations of the real line cannot act effectively on it.
problem Understanding the limitations of transformations on the real line.
method Analyzing the group of orientation-preserving quasi-isometries of the real line.
result The group of quasi-isometries of the real line cannot act effectively on the line.
Compact Lie groups have compact isometry groups with pseudo-Riemannian metrics.
problem Characterizing isometry groups of compact Lie groups with pseudo-Riemannian metrics.
method Analyzing left-invariant pseudo-Riemannian metrics on compact Lie groups.
result Isometry groups of compact Lie groups are compact.
Proper holomorphic isometries between Bergman domains are biholomorphisms.
problem Characterizing isometries between Bergman domains.
method New method from Information Geometry.
result Proper holomorphic local isometries are biholomorphisms.
Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.
problem Understanding the length of elements in PU(2,1) relative to special elliptic isometries.
method Generalizing the involution length of the complex hyperbolic plane, calculating the α-length of PU(2,1) and describing decompositions of isometries. result Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.
Computes Weyl group of Kähler toric manifold isometries.
problem Computing the Weyl group of Kähler toric manifold isometries.
method Analyzes the group of holomorphic isometries of a Kähler toric manifold with real analytic Kähler metric.
result Computed the Weyl group of the group of holomorphic isometries.
In this paper we study isometry-invariant Finsler metrics on inner product spaces over R or C, i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most g…
Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular. In this work we consider unimodular solvable Lie groups and pro…
Classifies certain graph 2-braid groups up to quasi-isometry.
problem Classifying 2-braid groups over graphs up to quasi-isometry.
method Using intersection complexes and right-angled Artin groups.
result Classifies 2-braid groups over graphs with circumference ≤ 1 up to quasi-isometry.
Maps preserve distances in non-positively curved spaces.
problem Understanding continuous maps between boundaries of Hadamard manifolds.
method Circumcenter extension maps, cross ratio preservation, visibility conditions.
result Circumcenter extension maps are rough isometries under certain conditions.
Study of isometries in spacetimes without observer horizons.
problem Understanding the symmetries of spacetimes without specific boundaries.
method Analysis of isometry groups in causal spacetimes without observer horizons.
result The group of time orientation-preserving isometries acts properly on the spacetime.
The paper explores conditions for constructing and extending infinitesimal isometries on special sub-Riemannian manifolds.
problem Finding conditions for infinitesimal isometries on special sub-Riemannian manifolds.
method Introducing $\is^*$-regular and $\is$-regular points to construct and extend infinitesimal isometries.
result Conditions on special sub-Riemannian manifolds allow for the construction and extension of infinitesimal isometries.
Bi-geodesic mappings preserve distances on hyperbolic surfaces with boundaries.
problem Preserving distances on hyperbolic surfaces with boundaries.
method Proving bijections between geodesics are isometries.
result A bijection between geodesics is an isometry.
We show that if a shrinking soliton is asymptotic to a cone along an end then the isometry group of the cross-section of the cone embeds in the isometry group of the end of the shrinker. We also provide sufficient conditions for the isometries of the end to extend to the entire shrinker.
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…
Lattices in PSL(2,C) are omnipotent, acting on geodesics and homology.
problem Understanding the full isometry groups of hyperbolic 3-manifolds and their lattices.
method Analyzing geodesics and applying the Virtual Special Theorems.
result Every non-arithmetic lattice in PSL(2,C) is omnipotent, acting on homology.
The study defines conditions for Finsler spacetime structures in (α,β)-metrics and identifies their isometries.
problem Conditions for Finsler spacetime structures in (α,β)-metrics. method Established necessary and sufficient conditions for Finsler spacetime structures.
result Identified (α,β)-Finsler spacetimes and determined the relation between isometries of (α,β)-metrics and the underlying pseudo-Riemannian metric. In this paper we develop a complete theory of factorization for isometries of hyperbolic 4-space. Of special interest is the case where a pair of isometries is linked, that is, when a pair of isometries can be expressed each as compositions of two involutions, one of which is common to both isometries. Here we develop …
Study describes isometry groups of specific Lie groups.
problem Understanding isometry groups of compact Lie groups.
method Analyzing bi-invariant metrics on SO(4) and U(n).
result Full groups of isometries identified for specific Lie groups.
Using an extension to isometries of the associated Sasaki structure, we establish a Lie transformation group structure for the set of isometries of a pseudo-Finsler conical metric.
The study shows finite measure-preserving isometry groups for certain metric measure spaces.
problem Understanding the structure of isometry groups in metric measure spaces.
method Analyzing synthetic negative Ricci curvature and Bakry-Émery Ricci curvature.
result The measure-preserving isometry group is finite for compact metric measure spaces with specific curvature conditions.
We show that isometries between open sets of Carnot groups are affine. This result generalizes a result of Hamenstadt. Our proof does not rely on her proof. In addition, we study global isometries of general homogeneous manifolds equipped with left-invariant subFinsler distances. We show that each isometry is determine…
We classify isometries of compact Lorentz manifolds.
problem Understanding the isometry group of compact Lorentz manifolds.
method Proving structure theorems and applying the Tits alternative.
result Classification of lattices acting on compact Lorentz manifolds.
Let S be an orientable surface of finite type and let Mod(S) be its mapping class group. We consider actions of Mod(S) by semisimple isometries on complete CAT(0) spaces. If the genus of S is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(S) on the completion of Teichm…
Quasi-isometries in horospherical products are close to product maps.
problem Understanding the rigidity of quasi-isometries in specific geometric spaces.
method Proving quasi-isometries are uniformly close to product maps in horospherical products of hyperbolic spaces.
result Quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid.