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 proofs”
Direct proof of weak compactness in Kähler Ricci flow.
problem Weak compactness in Kähler Ricci flow.
method Direct proof approach.
result Time-slice weak compactness on Fano manifolds.
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 .
Direct proof for all conformally flat isoparametric submanifolds in Euclidean space.
problem Classifying conformally flat isoparametric submanifolds in Euclidean space.
method Direct proof approach.
result Complete classification of conformally flat isoparametric submanifolds of Euclidean space.
Direct proofs of implications between three theorems on maps of simplex.
problem Understanding relations between three theorems on maps of simplex.
method Direct proofs using interesting relations between van Kampen and Conway-Gordon-Sachs numbers.
result Exhibited relations and direct proofs of implications between the theorems.
Direct proof of Neumann isoperimetric inequality for convex domains.
problem Neumann isoperimetric inequality on convex domains.
method Direct proof using Riemannian manifold properties.
result New proof of Neumann isoperimetric inequality.
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.
Direct proof given for a category of free groups.
problem Understanding the category of finitely generated free groups.
method Direct, combinatorial proof without Lawvere theories.
result Direct proof of the category being a PROP for commutative Hopf algebras.
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…
Direct proof of implication between geometric convex hull statements.
problem Deriving one geometric convex hull statement from another.
method Direct proof of implication between statements.
result Direct derivation of one geometric convex hull statement from another.
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 .
Direct proof of cohomology isomorphism for pullback Lie algebroids.
problem Cohomology of pullback Lie algebroids under surjective submersions.
method Differential-geometric proof, leafwise cohomology vanishing, exhaustion-and-patching argument.
result Cohomology isomorphism and injectivity properties for pullback Lie algebroids.
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.
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 …
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".
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…
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
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.
We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.
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 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…
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.
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.
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.
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.
New proof shows normal sub-Riemannian extremals locally minimize energy.
problem Understanding why normal sub-Riemannian extremals locally minimize energy.
method Provides a new proof without explicit use of local optimality and geometry.
result Explicitly shows the relation between the geometry and local optimality.
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.
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.
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.
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…
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.
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.
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.
Direct proof for Duflo isomorphism for arbitrary Lie algebras.
problem Duflo's theorem for finite dimensional Lie algebras.
method Topological proof using ribbon 2-knots and homomorphic expansions.
result Explicit formula for the Duflo map.
The paper studies curvature of geometric objects related to sheaves and line bundles.
problem Curvature of higher direct images of sheaves twisted by line bundles.
method Explicit curvature formulas derived for certain sheaves and line bundles.
result Proof of a result by Viehweg-Zuo in the context of a maximal variation family.