arXiv preprints from January 1, 2026 through September 19, 2026 — 21:51:04 EST
We prove an equivariant Landweber exact functor theorem for abelian compact Lie groups $G$. For a graded module $N$ over the $G$-equivariant Lazard ring $L_G$, we give necessary and sufficient algebraic conditions on $N$ for the functor \[ X\longmapsto (MU_G)_*(X)\otimes_{L_G} N \] to define a homology theory on the category...
A BV structure is constructed on the space of zero modes of a quadratic elliptic higher abelian gauge theory. The associated BV integral is shown to be independent of the choice of zero-mode Lagrangian under mild hypotheses. The construction yields explicit zero-mode partition functions for several $p$-form abelian gauge theories.
We bring new insights into the numerical geography of polarized Calabi-Yau threefolds through the first jet bundle, tangent geometry and projective duality. Let $X$ be a Calabi-Yau threefold with a very ample polarization $H$. We use mixed intersections on the projectivized dual of the first jet bundle to prove a quadratic inequality...
We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(Δ_{\mathbb{S}^2}+2)u=0$ on smooth spherical annuli with $u=0$ and $|\nabla u|=1$ on the boundary; their one-homogeneous extensions are the axially symmetric...
We study the singular limit $p \downarrow 1$ for positive radial entire solutions $u_p$ of $$ -Δ_p u_p=F_p\left(|x|, u_p,\left|\nabla u_p\right|\right) u_p^{-β_p} \quad \text { in } \mathbb{R}^n, $$ where $n \geq 2,1<p<\min \{2, \sqrt{n}\}$, and $0 \leq β_p \leq p-1$. Assuming that $$ F_p \rightarrow F_1 \quad \text { locally...
In this paper we study a linear drift perturbed by a superposition of $m$ independent fractional Brownian motions with known Hurst parameters and a common scale, observed at $N$ equidistant times. Inference for such models is usually asymptotic; we show that here it is exact. We derive the maximum likelihood estimators of the drift...
Feature-based multi-product pricing uses customer characteristics to identify demand heterogeneity and tailor prices across products. Choice model trees segment customers through interpretable feature rules and fit a demand model within each leaf. Existing methods typically construct these trees greedily, selecting one myopic split at...
This work addresses a longstanding gap in the statistical foundations of marginal maximum likelihood estimation for high-dimensional latent variable models. Marginal maximum likelihood estimation is widely used to fit latent variable models across the social sciences, ecology, and machine learning. Despite its broad use, rigorous...
Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture...
This paper develops an embedded-hybridized discontinuous Galerkin (E-HDG) method combined with a first-order implicit-explicit scalar auxiliary variable (IMEX-SAV) time discretization for variational initial-state data assimilation governed by the unsteady incompressible Navier-Stokes equations. We adopt an optimize-then-discretize...
We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n\geq 2$. More precisely, we show that if $(M^n,g)$ is a Cartan-Hadamard manifold satisfying $\mathrm{Sec}_g\leq\bar k\leq 0$ and $\mathrm{Ric}_g\geq...
The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by...
If ZFC is consistent, then so is ZF+DC+BPI+there is no Vitali set.
We continue to develop a theory of Besov and Triebel-Lizorkin spaces associated with weighted subcoercive operators on a real connected Lie group, specializing to the case of groups with polynomial volume growth. We consider the full scale of spaces and consider equivalent definitions, inclusions, discretization, and duality.
In the present paper, we study the maximization problem of the $k$-Torsional rigidity under quermassintegral constraint, with particular emphasis on the role of the ball. Our main result shows a phenomenon which, as far as we know, has not previously been observed: the ball, rather than being an extremal shape, is a saddle point. More...
The purpose of this paper is to extend an article by Hilhorst, Mimura and Sch{ä}tzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the...
We study complete stable minimal hypersurfaces in Riemannian manifolds under various curvature assumptions. In an $(n+1)$-dimensional complete oriented manifold with nonnegative scalar curvature, we prove that no complete oriented noncompact stable minimal hypersurface can be conformally equivalent to a bounded domain in an...
We study the problem of minimizing a weighted sum of squared Wasserstein distances with signed coefficients. In the case of a single positive coefficient, we derive two convex dual formulations: one expressed in terms of Brenier potentials, and one as a projection problem in convex order. Such dual formulations arise via Toland...
We classify finite-energy positive solutions to the Yamabe-type equation on the 15-dimensional octonionic Heisenberg group, whose algebra is non-associative. Extremals for the Folland-Stein-Sobolev inequality on this group are explicitly described. This confirms the conjecture of Garofalo and Vassilev [Duke Math. J. 2001] on the $15$...
Let $Δ_k$ be the Dunkl Laplacian associated with an arbitrary root system and a nonnegative multiplicity function. For every $0<p\leq1$, a Coifman-Weiss type atomic characterization of the Hardy space $H^p_{\mathrm{Dunkl}}$ is established. More precisely, it is proved that the space $H^p_{\mathrm{Dunkl}}$, which is originally defined...
We study the far-field behavior of solutions of the one-phase Bernoulli free boundary problem in the exterior of a ball, and of entire solutions with a single compactly supported inhomogeneity of the free boundary condition, which we call a defect. For solutions which blow down to a half-plane solution (proper solutions) we establish...
We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of paraductive...
We establish a weighted extension of the Bishop-Gromov volume comparison theorem for complete Riemannian manifolds with Ricci curvature bounded below. Given a point $p$ and positive radial weights $f$ and $h$, we consider the weighted volume of a geodesic ball and a corresponding model weighted volume in the simply connected space...
Let $U,V$ be matrix $\mathcal A_p$ weights, $1<p<\infty$, and let $B$ be a matrix-valued function. For Calderón--Zygmund operators $T$ with scalar standard kernels, we characterize boundedness and compactness of $[M_B,T\otimes I_m]:L^p(U)\to L^p(V)$ by two-matrix BMO and vanishing oscillation conditions. The converse statements...
We introduce forward recursive aggregator systems in It__o-diffusion markets, bridging the theories of recursive utilities and of forward performance criteria. We derive the associated HJB SPDE and sufficient conditions for consistency and admissibility. We also develop a convex duality theory based on state price densities and...