We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined and a condensed proof of the R/Z Grothendieck-Riemann-Roch theorem.
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48 results for “direct proof”
Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalismmath-ph
Direct proof of Alexander polynomial scaling for L-shaped representations.
problem Proving scaling property of Alexander polynomials for specific representations.
method Direct use of Reshetikhin-Turaev formalism to compute R-matrices.
result Normalized Alexander polynomial for one-hook representations scales with .
Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.
problem Proving the coisotropic embedding theorem for pre-symplectic manifolds.
method Recast geometric choice of connection as algebraic embedding into cotangent bundle, identify symplectic thickening as submanifold of Hamiltonian momenta conjugate to kernel directions.
result Alternative proof of the coisotropic embedding theorem.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
problem Division Theorem in Skoda's context
method Degeneration approach inspired by B. Berndtsson and L. Lempert's extension theorem
result Simplified and extended proof of extension theorem
The compression theorem Imath.GT
This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal field in Q X R. The theorem can be deduced from Gromo…
New proof of Grauert's theorem using differential geometry.
problem Proper holomorphic morphisms and coherence of higher direct images.
method Differential-geometric proof, antiholomorphic superconnection, Hironaka's desingularization.
result New proof of Grauert's theorem in both smooth and singular cases.
This article is based on the lectures given at the ``Ecole thematique de theorie ergodique'', at the C.I.R.M. in Marseille, in April 2006. We give a complete proof of a theorem of Kerckhoff, Masur and Smillie on the unique ergodicity of the directional flow on a translation surface in almost every direction. The proof …
New proof for complex 3D shapes.
problem Complex 3D shapes with infinite fundamental groups.
method Direct proof using finite covers.
result Every shape has a simpler version.
Direct proof of hyperbolicity for a family of knots.
problem Proving the hyperbolicity of a family of knots.
method Using a theorem of Casson and Rivin, constructing geometric triangulations.
result Direct proof of hyperbolicity for -pretzel knots and links with .
A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived.
Supplement to "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs"stat.ML
This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and …
In this note we obtain the characterization for asymptotic directions on various subgroups of the diffeomorphism group. We give a simple proof of non-existence of such directions for area-preserving diffeomorphisms of closed surfaces of non-zero curvature. Finally, we exhibit the common origin of the Monge-Ampere equat…
We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.
A proof that hyperbolic plane cannot be immersed in Euclidean 3-space.
problem Proving the impossibility of isometrically immersing the hyperbolic plane in Euclidean 3-space.
method Applying ideas from undergraduate mathematics, including moving frames and connection forms, to simplify the proof.
result A key transition from principal directions to asymptotic directions simplifies the proof and yields a coordinate system.
Proof that Ricci flow preserves full holonomy group.
problem Invariance of full holonomy group under Ricci flow.
method Direct proof using invariance of reduced holonomy.
result Full holonomy group is invariant under Ricci flow.
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem [The compression theorem I; 4.7], arxiv:math.GT/9712235.
We provide a direct proof of time-slice weak compactness along the Kähler Ricci flow on Fano manifolds.
In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.
We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes allowing for a useful integration theory consists precisely of those processes which can be written in the form , where is a local martingale and is a finite variation proce…
We give a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations including the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman…
Direct proofs are given of Juhl's formulae for GJMS operators and Q-curvatures starting from the original construction of GJMS.
Expanders and Property Amath.GT
We give a cohomological characterisation of expander graphs, and use it to give a direct proof that expander graphs do not have Yu's property A.
An elementary proof found for the double bubble problem in a specific norm.
problem Finding the shapes that minimize perimeter for given volumes in a specific norm.
method Direct comparison to a small family of parameterized sets for analysis.
result Existence of minimizing sets for any volume ratio parameter.
Simplified proof of spin^c structures using twistor spaces.
problem Proving every compact oriented 4-manifold admits spin^c structures.
method Using twistor spaces to provide a simpler, more geometric proof.
result Simplified and clarified understanding of spin^c structures in 4-manifolds.
We present a new and direct proof of the local Neumann isoperimetric inequality on convex domains of a Riemannian manifold with Ricci curvature bounded below.
Study on algebraic fiber spaces and their anti-canonical divisors.
problem Understanding positivity conditions and base loci of algebraic fiber spaces.
method Algebraic and analytic methods for positivity of direct image sheaves.
result Algebraic fiber spaces with semi-ample relative anti-canonical divisor have a product structure.
We know that any element of the exceptional Jordan algebra $\gJ$ is transformed to a diagonal form by the compact exceptional Lie group . However, its proof is used the method which is reduced a contradiction. In this paper, we give a direct and constructive proof.
We give a direct geometric proof of a Danilov-type formula for toric origami manifolds by using the localization of Riemann-Roch number.
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
Two proofs of Kalman Theorem using flows of vector fields.
problem Classical result of Control Theory (Kalman Theorem).
method Two proofs using flows of vector fields.
result New criteria for local controllability of non-linear systems.
Paper proves direct image sheaf positivity for certain Kähler fibrations.
problem Proving positivity of direct image sheaves for Kähler fibrations.
method Uses singular Hermitian line bundles and Narasimhan-Simha metric.
result Direct image sheaf is singular Nakano semi-positive.
A simple proof shows standard billiard for certain convex domains.
problem Characterizing billiards in convex domains that are both projective and Minkowski.
method Direct simple proof in -smoothness, semi-local and local versions proved.
result Standard Euclidean billiard in an appropriate structure.
We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Sch{ö}nflies theorem. As an application, we show that one can read off oriented matroids from arrangement…
We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n=2) leads to a direct proof of Onofri inequality on S^2.
We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently separated at infinity must intersect at a finite point. The proof is based on a localized version of the Reilly formula applied to a suitable f-harmonic function with controlled gradient. In the immersed case, a new direct proof …
Geometric proof of contractibility of unitary group in strong topology.
problem Contractibility of unitary group in strong operator topology.
method Direct geometric proof and construction of special subspaces and operators.
result Direct geometric proof of contractibility theorem.
Given a special Kahler manifold M, we give a new, direct proof of the relationship between the quaternionic structure on its cotangent bundle and the variation of Hodge structures on the complexification of TM.
Entire scalar curvature flow and hypersurfaces of constant scalar curvature in Minkowski spacemath.DG
We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacel…
In this paper I give new elementary proofs of basic results of Gelfand, Kapranov and Zelevinskywhich express discriminants and resultants in terms of determinants of direct images of Cayley-Koszul complexes of sheaves.
We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.
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.
Direct proof shows adaptive gradient descent converges near-linearly for convex functions.
problem Proving near-linear convergence of adaptive gradient descent for convex functions.
method Direct Lyapunov-based argument for convex functions with unique minimizer.
result Direct proof of near-linear convergence for convex functions.
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, especially in case where the said line bundle satisfies a natural curvature assumption. …
Frank and Lieb proved sharp Sobolev inequalities without rearrangements.
problem Proving sharp Sobolev inequalities for function spaces.
method Using conformal covariance and commutator identities from the Fefferman-Graham ambient metric.
result Direct proof of sharp Sobolev inequalities and new nonlinear inequality.
We generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of those in \cite{MinhGaussian2010}.
Paper shows DMS as an EM algorithm with improved convergence.
problem Improving the convergence of DMS algorithm.
method Shows DMS as a generalized EM algorithm and provides new proofs.
result Demonstrates global convergence and linear convergence of DMS.