A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Maps between Hadamard manifolds are quasi-isometric to harmonic maps.
Study characterizes quasi-isometric embeddings of maps from cusped surfaces into moduli space.
Study on isometric submanifolds with preserved Gauss map metrics.
New corrugation process solves -isometric maps with conical singularities.
We prove that a quasi-isometric map, and more generally a coarse embedding, between pinched Hadamard manifolds is within bounded distance from a unique harmonic map.
Smoothly embed maps with controlled curvature errors.
The study examines when mapping class groups are quasi-isometric to graphs of curves.
The paper examines isometric timelike surfaces in 4D Minkowski space.
New groups are hyperbolic and rigid in mapping class groups.
Heat kernels map RCD spaces to Riemannian manifolds.
We show that for every quasi-isometric map from a Hadamard manifold of pinched negative curvature to a locally compact, Gromov hyperbolic, -space there exists an energy minimizing harmonic map at finite distance. This harmonic map is moreover Lipschitz. This generalizes a recent result of Benoist-Hulin.
Nonorientable surface mapping class group embeds quasi-isometrically in its orientable cover.
We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmuller space is a quasi-isometric embedding for both of the standard metrics. As a …
In this paper we investigate the existence of ``partially'' isometric immersions. These are maps f:M->R^q which, for a given Riemannian manifold M, are isometries on some sub-bundle H of TM. The concept of free maps, which is essential in the Nash--Gromov theory of isometric immersions, is replaced here by that of H-fr…
Study stability of rigid motions and Möbius transformations on spheres, proving new rigidity estimates.
Proves isometric embeddings in Euclidean spaces for RCD spaces.
We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic) link with five components.
Isometric embeddings of Teichmüller spaces are derived from branched coverings.
A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, rank 1 CAT(0) groups, mapping class groups and Out(Fn). As an application, we show that mapping clas…
Study isometric immersions in 3D Lie groups, proving new characterizations and classifications.
In these lecture notes, we combine recent homological methods of Kevin Whyte with older dynamical methods developed by Benson Farb and myself, to obtain a new quasi-isometric rigidity theorem for the mapping class group MCG(S) of a once punctured surface S of genus at least 2: if K is a finitely generated group quasi-i…
We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-…
Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the actio…
Study of graphs from hexagon decompositions of surfaces.
Wextend the results obtained recently by G. D'Ambra and A. Loi towards the proof of a conjecture of M.Gromov on isometric immersions via non-free maps.
We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a product of quasi-isometric embeddings into irreducible symmetric spaces. We thu…
The paper defines a universal Teichmüller space for PGL_d(R) and proves its properties.
Topology of isometric classes and flows of geometric structures
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms …
Holomorphic curves in moduli spaces are quasi-isometrically immersed.
This paper extends boundary embedding results to coarsely convex spaces.
We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either by puncturing a closed surface or via orbifold coverings. As a corollary, we give new quasi-isometric embeddings between mapping class groups.
Let S be an oriented surface of finite type of genus g with m punctures and where 3g-3+m>1. We show that the mapping class group M(S) of S is quasi-isometrically rigid. We also give a different proof of the following result of Behrstock and Minsky: The homological dimension of the asmyptotic cone of M(S) of S equals 3g…
A triharmonic map is a critical point of the 3-energy in the space of smooth maps between two Riemannian manifolds. We study a triharmonic isometric immersion into a space form of non-positively constant curvature. We show that if the domain is complete and both the 4-enegy and the L^4-norm of the tension field are fin…
Harmonic maps between pinched Hadamard surfaces are quasi-conformal.
New result on group actions in CAT(0) spaces with vanishing escape rate.
It is known that PQ-symmetric maps on the boundary characterize the quasi-isometry type of visual hyperbolic spaces, in particular, of geodesically complete \br-trees. We define a map on pairs of PQ-symmetric ultrametric spaces which characterizes the branching of the space. We also show that, when the ultrametric spac…
First explicit isometric immersion of a flat Klein bottle in 3D space.
We study the global property of local holomorphic isometric mappings from a class of Kahler manifolds into a product of projective algebraic manifolds with induced Fubini-Study metrics, where isometric factors are allowed to be negative.
Mapping class group subgroups yield quasi-isometric curve complex.
Random quotients of mapping class groups have rigid properties.
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples of pseudo biharmonic maps will be given.
Generalizes skyrmion theory to gauged maps with -action.
Proves unique maps from certain spaces to others.
The paper improves the approximation of isometric immersions in high codimension.
Study fourth-order geometric flow of shape operator for co-dimension one immersions.
Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the `elliptic' case.