24 citations · 72 across the 19 of their papers we have counts for
23 papers
Covariance and Principal Component Analysis on Riemannian Manifolds and Graphs
Luiz Hartmann, Wenwen Li, Washington Mio
We develop notions of covariance and principal component analysis (PCA) for probability measures on Riemannian manifolds of bounded geometry and a discrete counterpart for distribu…
An Atiyah-Bott formula for the Lefschetz number of a singular foliation
Luiz Hartmann, Gerardo A. Mendoza
This paper presents a formula for the Lefschetz number of a geometric endomorphism in the style of the Atiyah-Bott theorem. The underlying data consist, first, of a compact manifol…
Divided Differences and Multivariate Holomorphic Calculus
Luiz Hartmann, Matthias Lesch
We review the multivariate holomorphic functional calculus for tuples in a commutative Banach algebra and establish a simple "naïve" extension to commuting tuples in a general Bana…
Cheeger-Müller theorem for a wedge singularity along an embedded submanifold
Luiz Hartmann, Boris Vertman
In this paper we equate the analytic and the intersection Reidemeister torsions on spaces with a specific type of wedge singularities, which arise by turning the disc cross-section…
On the anomaly terms in Cheeger-Müller theorem on spaces with conical singularities
Luiz Hartmann, Mauro Spreafico
We prove that the anomaly term appearing in the ratio between Reidemeister torsion and analytic torsion for a space with a conical singularity vanishes in the smooth case. Moreover…
Zeta and Fredholm determinants of self-adjoint operators
Luiz Hartmann, Matthias Lesch
Let be a self-adjoint invertible operator in a Hilbert space such that is -summable. Under a certain discrete dimension spectrum assumption on , we study the rel…
Normalized Yamabe flow on manifolds with bounded geometry
Bruno Caldeira, Luiz Hartmann, Boris Vertman
The goal of this paper is to study Yamabe flow on a complete Riemannian manifold of bounded geometry with possibly infinite volume. In the case of infinite volume, standard volume…
Newton Polyhedra and Whitney Equisingularity for Isolated Determinantal Singularities
Thaís M. Dalbelo, Luiz Hartmann, Maicom Varella
Using Newton polyhedra and non-degeneracy of matrices we present conditions which guarantee the Whitney equisingularity of families of isolated determinantal singularities.
On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces
Alexandre Paiva Barreto, Francisco Fontenele, Luiz Hartmann
We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space , , defined by polynomials of odd…
Curvature estimates for graphs in warped products
Alexandre Paiva Barreto, Fabiani A. Coswosck, Luiz Hartmann
We prove local and global upper estimates for the infimum of the mean curvature, the scalar curvature and the norm of the shape operator of graphs in a warped product space. Using…
Intersection torsion and analytic torsion of spaces with conical singularities
Luiz Hartmann, Mauro Spreafico
We prove an extension of the Cheeger-Müller theorem to spaces with isolated conical singularities: the -analytic torsion coincides with the Ray-Singer intersection torsion on…
Rotational Surfaces with second fundamental form of constant length
Alexandre P. Barreto, Francisco Fontenele, Luiz Hartmann
We obtain an infinite family of complete non embedded rotational surfaces in whose second fundamental forms have length equal to one at any point. Also we prove that…
Resolvent Trace Asymptotics on Stratified Spaces
Luiz Hartmann, Matthias Lesch, Boris Vertman
Let be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian …
On the domain of Dirac and Laplace type operators on stratified spaces
Luiz Hartmann, Matthias Lesch, Boris Vertman
We consider a generalized Dirac operator on a compact stratified space with an iterated cone-edge metric. Assuming a spectral Witt condition, we prove its essential self-adjointnes…
Brasselet number and Newton polygons
Thais M. Dalbelo, Luiz Hartmann
We present a formula to compute the Brasselet number of $f:(Y,0)\to (\C, 0)$ where is a non-degenerate complete intersection in a toric variety . As applications we…
Zeta-determinants of Sturm-Liouville operators with quadratic potentials at infinity
Luiz Hartmann, Matthias Lesch, Boris Vertman
We consider Sturm-Liouville operators on a half line , with potentials that are growing at most quadratically at infinity. Such operators arise naturally in the an…
The analytic torsion of the finite metric cone over a compact manifold
L. Hartmann, M. Spreafico
We give an explicit formula for the analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the dif…
The boundary term from the Analytic Torsion of a cone over a -dimensional sphere
Luiz Hartmann
We present a direct proof that the Anomaly Boundary term of J. Brünning and X. Ma generalizes to the cases of the cone over a -dimensional sphere.
R torsion and analytic torsion for a conical frustum
Luiz Hartmann, Mauro Spreafico
We investigate the limit the R torsion of a conical frustum as one of the basis is shrunk to a point. We show that, if we take suitable regularization, such a limit gives the inter…
An extension of the Cheeger-Müller theorem for a cone
Luiz Hartmann, Mauro Spreafico
We prove the equality of the -analytic torsion and the intersection R torsion of the even dimensional finite metric cone over an odd dimensional compact manifold.
The Analytic Torsion of the cone over an odd dimensional manifold
L. Hartmann, M. Spreafico
We study the analytic torsion of the cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the con…
The analytic torsion of a cone over a sphere
L. Hartmann, M. Spreafico
We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere.
Reidemeister torsion and analytic torsion of discs
L. Hartmann, T. de Melo, M. Spreafico
We study the Reidemeister torsion and the analytic torsion of the dimensional disc in the Euclidean dimensional space, using the base for the homology defined by Ray and Si…