arXiv research

Proves real analyticity on surfaces based on restrictions.

In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent. In dimension four, the quaternionic analytic torsion equals to the self-dual an…

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…

Transforms uniquely determine Higgs fields on real-analytic manifolds.

We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no corners. Additionally our approach uses a different construction.

Geometric analysis on real analytic manifolds using seminorms.

Analyzes properties of Hopf manifolds from analytic and metric perspectives.

Analytic metrics are uniquely determined by their scattering map.

Proves Lorentzian manifold properties for analytic 3D spaces.

We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…

Formula connects analytic and Reidemeister torsions for hyperbolic manifolds.

We deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known whether holomorphic star products exist on complex analytic manifolds. The main p…

The article consists of a survey on analytic and topological torsion. Analytic torsion is defined in terms of the spectrum of the analytic Laplace operator on a Riemannian manifold, whereas topological torsion is defined in terms of a triangulation. The celebrated theorem of Cheeger and Müller identifies these two noti…

Given any real-analytic CR manifold M, we provide general conditions on M guaranteeing that the group of all its global real-analytic CR automorphisms is a Lie group (in an appropriate topology). Our conditions are in particular satisfied when M is an arbitrary compact real-analytic hypersurface embedded in some Stein …

Real analytic submersion images are always real analytic.

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…

Finite totally geodesic hypersurfaces in curved manifolds proven.

Examines a new type of analytic torsion on Riemannian manifolds.

The paper solves equations for Higgs bundles on non-Kähler manifolds.

Study proves rigidity results for analytic spacetimes without boundary or timelike boundary.

New tools for analyzing Kähler manifolds, proving operator algebra and asymptotic kernel.

Analytic sub-Riemannian geodesics in 3D are always C1 and analytic except finitely many points.

The paper proves conditions for compact complex manifolds to be Kahler outside analytic subsets.

Constructs equivariant analytic torsion for proper actions on manifolds.

Classifies real-analytic SL(n,R) actions on closed manifolds.

Analytic Euler fields on non-torus bundles have periodic orbits.

In a previous article, analytic 1-submanifolds had been classified w.r.t. their symmetry under a given regular and separately analytic Lie group action on an analytic manifold. It was shown that such an analytic 1-submanifold is either free or (via the exponential map) analytically diffeomorphic to the unit circle or a…

The paper provides conditions for smooth CR-manifolds to be CR-diffeomorphic to real-analytic ones.

Analytic torsion defined for rank 2 distributions on 5-manifolds.

Let M be a real analytic manifold modeled on a locally convex space and K be a non-empty compact subset of M. We show that if an open neighborhood of K in M admits a complexification which is a regular topological space, then the germ of the latter (as a complex manifold) is uniquely determined. If M is regular and the…

We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without boundary. We now derive a gluing formula for our construction, which can be viewed as…

Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.

Develops Bialynicki-Birula and Morse-Bott theory for complex analytic spaces.

Let (M,g) be an analytic, compact, Riemannian manifold with boundary, of dimension n >= 2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition [23]. Using analytic microlocal analysis, we prove a microlocal regularity theorem for ge…

Paper constructs an invariant for a specific type of complex manifolds.

GAMLA learns manifold structures with auto-encoding for global insights.

We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analyti…

Defines hypercomplex analytic spaces and schemes.

Uniqueness proof for Calderón's problem on real-analytic vector bundles.

This paper is devoted to a proof of a generalized Ray-Singer conjecture for a manifold with boundary (the Dirichlet and the Neumann boundary conditions are independently given on each connected component of the boundary and the transmission boundary condition is given on the interior boundary). The Ray-Singer conjectur…

On a Hermitian manifold we construct a symmetric $(1,1)$- tensor $H$ using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor $H$ for a harmonic $1$-form to be analytic and for an analytic $1$-form to be harm…

We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumption, this can happen only on topological spheres.

We present the complex analytic and principal complex analytic realizability of a link in a 3-manifold $M$ as a tool for understanding the complex structures on the cone $C(M)$.

Analyzes the Levi form on CR manifolds of any dimension.

The paper equates the index of a vector bundle to the manifold's index and introduces an analytic torsion.

The paper classifies actions of a specific group on certain manifolds.

Functional-analytic method for stochastic parallel transport in bundles.