Sep 2026· Journal of Topology and Analysis (JTA)· pp. 1-64· 0 citations
Abstract
We generalize the construction of the Bismut superconnection to the non-integrable setting of subRiemannian manifolds equipped with a transverse distribution. The non-integrability produces singularities within the superconnection, and it is shown that if one extracts the finite part then the resulting operator is hypoelliptic on two-step subRiemannian manifolds. Moreover, it is shown that a perturbation produces a hypoelliptic operator on any subRiemannian manifold. The explicit form of the operator on principal circle bundles is computed and its kernel is determined for principal circle bundles over the [Formula: see text]-sphere with conformal curvature. A discussion of possible directions for generalizations and open questions follows; in the direction of index theory we introduce matrix twisted Clifford relations in the transverse directions to produce asymptotic superconnections with non-vanishing Fredholm index. We conclude with a possible relationship between our hypoelliptic operator and a constrained supersymmetric sigma model.
In this article we reconsider the proof of subelliptic estimates for Geometric Kramers–Fokker–Planck operators, a class which includes Bismut’s hypoelliptic Laplacian, when the base manifold is closed (no boundary). The method is significantly different from the ones proposed by Bismut–Lebeau in [BL08] and Lebeau in ...
F. Nier, Xing-Feng Sang, Francis White· Annales Henri Lebesgue· 0 citations
We prove two supercongruence conjectures of Li--Long--Tu concerning truncated very-well-poised ${}_7F_6(1)$ series and Fourier coefficients of modular forms. The proofs are based on a common deformation method. By deforming the original truncated hypergeometric series to suitable terminating series, we are able to appl...
We formulate the extremization problem for codimension-two hypersurfaces in de Sitter space in holomorphic coordinates, with real anchoring conditions at future infinity. The resulting equation ($K^I=0$) describes complex bulk realizations extending the usual piecewise Hartle--Hawking construction. We compute holograph...
G. Anastasiou, Ignacio J. Araya, Avijit Das et al.· 0 citations
This corrigendum corrects an error in the proof of Theorem 6.20 of the original article. Property (P), used to propagate umbilicity from the initial spacelike submanifold to the lightlike hypersurface generated by the normal exponential map, is false, and an explicit counterexample shows that the corresponding implic...
J. Gómez· Classical and quantum gravit...· 0 citations
We resolve four questions concerning Karpukhin's Dirichlet-to-Neumann operator on differential forms. First, for $0\leq p\leq n-2$, we prove that the operator is classical pseudodifferential of order one and compute its principal symbol, which is elliptic on the coclosed symbol space. This answers Open Question 7.19 in...
We prove categorical Torelli theorems for ordinary and weighted hypersurfaces using the singularity category of the completed affine cone. For Fano hypersurfaces we use the Kuznetsov component, whereas for hypersurfaces of general type we use the full category of graded matrix factorizations. When the degree is coprime...
