arXiv research

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal exponential map on the finite boundary. As a main application, a normal fo…

Paper studies the full asymptotic torsion forms of flat bundles.

Study of torsion forms for positive line bundles.

Study characterizes conformal boundaries of de Sitter spacetimes.

Defines height pairing for differential forms on Riemann surface degenerations.

Geodesic X-ray transform proves injective for smooth one-forms on gas giant manifolds.

Study leading-order asymptotics for VIX option prices in Bergomi models.

We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.

Study short-maturity VIX and European option prices with jumps.

Study asymptotic behavior of second Chern forms on degenerating Kähler-Einstein surfaces.

The paper proves rigidity for shells in non-Euclidean spaces.

Analytic torsion expansions for symmetric and complex homogeneous spaces.

Projective pre-compactness induces projective structure on boundary, relates to GR asymptotic forms.

Estimates holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds.

We prove a spanning result for vector-valued Poincaré series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$, we provide estimates for the norms of these automorphic forms and we find asymptotics of…

New tensors help determine if metrics are related to Poincaré-Einstein ones.

Let $φ\in C^\infty(\Complex^n)$ be a given real valued function. We assume that $\pr\ddbarφ$ is non-degenerate of constant signature $(n_-,n_+)$ on $\Complex^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2kφ}$, $k>0$, admits a full asymptotic expansi…

We show that the mass of an asymptotically hyperbolic manifold with a noncompact boundary can be evaluated via the Ricci tensor and the second fundamental form by using purely coordinates. The method is analog to Miao-Tam's approach to the asymptotically flat manifold.

We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recentl…

Formula derived for torsion of modified Dirac operator.

In this note, we prove the regularity of eta forms by the Clifford asymptotics. Then we generalize this result to the equivariant case.

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove…

We develop an efficient method to calibrate CDS spreads using asymptotic approximations.

This contribution summarizes the results on the asymptotic performance of several variants of the FastICA algorithm. A number of new closed-form expressions are presented.

New insights into manifold properties using Seiberg-Witten and $L^2$ harmonic theories.

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…

The purpose of this paper is first to give an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with increasing powers of a given line bundle. Secondly, we generalize this formula, thanks to the theory of Toeplitz operators, in the case where the powers of the line bundle is replac…

Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.

In this paper we investigate the rigidity of ancient solutions of the mean curvature flow with arbitrary codimension in space forms. We first prove that under certain sharp asymptotic pointwise curvature pinching condition the ancient solution in a sphere is either a shrinking spherical cap or a totally geodesic sphere…

We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general…

The study shows that certain nearly G2 and nearly Kähler conifolds cannot be resolved by gluing asymptotically conical G2 and Calabi-Yau manifolds.

Study Cayley fibrations on Bryant-Salamon $Spin(7)$ manifolds.

Let Y be a compact, oriented 3-manifold with a contact form a. For any Dirac operator D, we study the asymptotic behavior of the spectral flow between D and D+cl(-ira) as r very large. If a is the Thurston-Winkelnkemper contact form whose monodromy is the product of Dehn twists along disjoint circles, we prove that the…

The paper studies the distribution of random degeneracy sets on complex manifolds.

Ricci flow modelled on specific singularities on closed manifolds.

We introduce the notion of an asymptotically Poincaré family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel convex surfaces, and that the asymptotic behavior of the first and second fundamental forms determines the projective struc…

There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence method, pseudo-likelihood, Monte Carlo maximum likelihood, and noise contrastive…

Study on minimal submanifolds in curved spaces with unique solution to asymptotic Plateau problem.

This paper studies mean curvature flows near cylindrical singularities.

The paper proves the stability of a flow in Schwarzschild space.

We construct a form of swallowtail singularity in R^3 which uses coordinate transformation on the source and isometry on the target. As an application, we classify configurations of asymptotic curves and characteristic curves near swallowtail.

Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold $(M^3, g)$ with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature has an explicit bound in form of asymptotic volume ratio.

WSINDy algorithm proves robust to noise in identifying differential equations.

New method for spectral and Bergman kernels under local spectral gap condition.

The study investigates the consistency of $k$-means clustering under finite expectation assumptions.

$\mathcal{H}-$holomorphic curves are solutions of a specific modification of the pseudoholomorphic curve equation in symplectizations involving a harmonic $1-$form as perturbation term. In this paper we study the asymptotics of $\mathcal{H}-$holomorphic curves defined on a sequence of degenerating cylinders.

Study linear differential operators on special manifolds.

Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and the…