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.
Paper characterizes a special hypersurface in 5D sphere.
The paper proves conditions for closed minimally immersed hypersurfaces in a 5-sphere.
Convex hypersurfaces in curved spaces bound convex regions.
The paper derives inequalities for mean curvatures of hypersurfaces in Riemannian manifolds.
We study stability properties of -minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the top…
In this paper, we study isoparametric hypersurfaces in Finsler space forms by investigating focal points, tubes and parallel hypersurfaces of submanifolds. We prove that the focal submanifolds of isoparametric hypersurfaces are anisotropic-minimal and obtain the Cartan-type formula in a Finsler space form with vanishin…
Survey of Cartan's work on isoparametric hypersurfaces in spheres.
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.
Survey of Cartan and Münzner's work on isoparametric hypersurfaces.
Paper classifies hypersurfaces in a sphere with specific curvature properties.
In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore,…
Surveying isoparametric hypersurfaces in spheres, focusing on Élie Cartan's techniques.
This paper provides many examples of Sbrana-Cartan hypersurfaces.
The paper proves properties of specific hypersurfaces in a 5-sphere.
Total curvatures of certain hypersurfaces are continuous.
Lightlike manifolds studied via Cartan geometries in Lorentz-Minkowski spacetime.
New classification of hypersurfaces with conformal variations.
Study shows curvature bounds for convex hypersurfaces in specific manifolds.
Solves Plateau problem for surfaces in pinched curvature manifolds.
Study geometrical properties of Finsler space hypersurface with h-Matsumoto change.
The study extends isoperimetric inequalities to non-positive curvature spaces.
We introduce analogues of a map due to Rossi and show how they can be used to explicitly determine all covers of certain homogeneous strongly pseudoconvex 3-dimensional hypersurfaces that appear in the classification obtained by E. Cartan in 1932.
The paper studies inverse mean curvature flow on hypersurfaces in space forms.
We explicitly determine the structure equations of 5-dimensional Levi 2-nondegenerate CR hypersurfaces, using our recently constructed canonical Cartan connection for this class of CR manifolds. We also give an outline of the basic properties of absolute parallelisms and Cartan connections, together with a brief discus…
In this paper we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson-Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersu…
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an introduction of the classical Poincare-Cartan form in the context of EDS, follow…
Sharp curvature inequality extends Euclidean isoperimetric inequality to Cartan-Hadamard manifolds.
We formulate the equivalence problem, in the sense of E. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form …
We provide an explicit description of all rigid hypersurfaces that are equivalent to a Heisenberg sphere. These hypersurfaces are determined by 4 real parameters. The defining equations of the rigid spheres can also be viewed as the complete solution of a non-linear PDE that expresses the vanishing Cartan curvature con…
This paper extends classifications of hypersurface immersions to higher dimensions.
We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus, Karcher, and Münzner. This completes the classification of isoparametric hypersurfaces in spheres that É. Cartan initiated…
We show that the boundaries of thin strongly pseudoconvex Grauert tubes, with respect to the Guillemin-Stenzel Kähler metric canonically associated with the Poincaré metric on closed hyperbolic real-analytic surfaces, has nowhere vanishing Cartan CR-curvature. This result provides a wealth of examples of compact -di…
We study the asymptotic Dirichlet problem for -minimal graphs in Cartan-Hadamard manifolds . -minimal hypersurfaces are natural generalizations of self-shrinkers which play a crucial role in the study of mean curvature flow. In the first part of this paper, we prove the existence of -minimal graphs with pre…
3-manifolds with convex boundary are rigid in certain curvature conditions.
We develope in great computational details the classical Cartan equivalence problem for Levi-nondegenerate C^6-smooth real hypersurfaces M^3 in C^2, performing all calculations effectively in terms of a (local) graphing function \varphi. In particular, we present explicitly the unique (complex) essential invariant J of…
New entropy functionals for curved spaces help predict shape behavior.
A new direct construction method for Cartan-Moser chains.
Biconservative hypersurfaces are hypersurfaces with conservative stress-energy tensor with respect to the bienergy functional, and form a geometrically interesting family which includes that of biharmonic hypersurfaces. In this paper we study biconservative surfaces in the 3-dimensional Bianchi-Cartan-Vranceanu spaces,…
We are studying a relationship between isoparametric hypersurfaces in spheres with four distinct principal curvatures and the moment maps of certain Hamiltonian actions. In this paper, we consider the isoparametric hypersurfaces obtained from the isotropy representations of compact irreducible Hermitian symmetric space…
We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any compact symmetric space. Our second objective is to investigate such hypersurfa…
The concept of h-vector was introduced by H. Izumi in 1980. Recently we have obtained the Cartan connection for the Finsler space whose metric is given by Kropina change with an h-vector. In 1985, M. Matsumoto studied the theory of Finsler hypersurface. In this paper, we derive certain geometrical properties of a Finsl…
In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric starting from a variational problem on hypersurfaces in an -dimensional manifold . This distance depends not only of the point $\textsc{m}\in\mathcal{M}$ but on the orient…
New examples of austere submanifolds and hypersurfaces with specific curvature properties.
Survey on minimal surface equation on Cartan-Hadamard manifolds.
New classification of complex hypersurfaces using advanced algebraic methods.
We give an introduction to the theory of varieties of minimal rational tangents, emphasizing its aspect as a fusion of algebraic geometry and differential geometry, more specifically, a fusion of Mori geometry of minimal rational curves and Cartan geometry of cone structures.
E. Cartan proved that conformally flat hypersurfaces in S^{n+1} for n>3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n-1)-spheres. We prove that the Gauss-Codazzi equation for conformally flat hypersurfaces in S^4 is a soliton equation, and use a dressing action from sol…
Totally biharmonic hypersurfaces in space forms and 3D BCV spaces classified.