Related papers: Analytic torsion forms for fibrations by projectiv…
The spectrum of the Laplace-Dolbeault operator for any line bundle with parallel curvature on a flat complex torus is computed. The Ray-Singer analytic torsion is then deduced, generalizing thus Bost's result for ample line bundles and…
General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…
In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas,…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
This paper contains a long summary of the basic properties of higher FR torsion. An attempt is made to simplify the constructions from my book Higher Franz-Reidemeister Torsion (IP/AMS Studies in Advanced Math 31). Some new basic theorems…
Arakelov-Parshin rigidity is concerned with varieties mapping rigidly to the moduli stack M_h of canonically polarized manifolds. Affirmative answer for any class of maps implies finiteness of the given class. This article studies…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…
We construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also construct a surface with a unique rational point and the…
In this paper we define a regularized version of the analytic torsion for arithmetic quotients of the symmetric space SL(n,R)/\SO(n). The definition is based on the study of the renormalized trace of the corresponding heat operators, which…
In this paper, we study a deformation theory of rigid analytic spaces. We develop a theory of cotangent complexes for rigid geometry which fits in with our deformations. We then use the complexes to give a cohomological description of…
We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, A_t(G) of finite injective…
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the…
In this paper we study the analytic torsion of an odd-dimensional manifold with isolated conical singularities. First we show that the analytic torsion is invariant under deformations of the metric which are of higher order near the…
In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter…
This paper provides a complete classification of torus-invariant curves in Cherkis bow varieties of type A. We develop combinatorial codes for compact and noncompact invariant curves involving the butterfly diagrams, Young diagrams, and…
In this work, we derive a set of compact analytical formulas expressing the three-dimensional acoustic radiation torque (ART) exerted on a particle of arbitrary shape embedded in a fluid and insonified by an arbitrary acoustic field. This…
We derive analytically some general features of the power-law sensitivity curve. They include an exact parametric equation, a formula for the peak sensitivity and a proof of convexity in log-log plot. A few conceptual points are also…
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.
This paper reports a method allowing for the determination of the shape of deformed fiber-like objects. Compared to existing methods, it provides analytical results including the local slope and curvature which are of first importance, for…