135 papers
This paper proves the existence of closed embedded minimal hypersurfaces with topology in by constructing them via a generalized rotational ansatz from any isoparametric hypersurface , thereby extending known minimal hypertori examples to a broader class of topologies.
This paper investigates nonconvex real-valued functions whose truncations become quasiconvex or convex beyond a certain level, with a specific focus on -smooth functions whose level sets lie within the positive definite region of their Hessian matrices, demonstrating the injectivity of their restricted gradients in that region.
This paper investigates the singularities and striction curves of two-ruled hypersurfaces in Euclidean four-space by introducing the concept of pseudo-non-degeneracy and analyzing the geometric relationship between these hypersurfaces and their generating curves via Frenet-type frames and height functions.
This paper presents a unified and simplified method, leveraging the Polydisc Theorem and prior work by Domin, Toledo, Clerc, and Ørsted, to calculate the Gromov norm of the Kähler class for all bounded symmetric domains, establishing that the norm is achieved if and only if the associated triangle is ideal with vertices on the Shilov boundary.
This paper introduces 0-shifted cosymplectic structures on differentiable stacks to develop a Hamiltonian action theory that includes a reduction procedure, a Kirwan convexity theorem, and examples of Morse-Bott Lie groupoid morphisms.
This paper extends fundamental volume comparison theorems in Riemannian geometry to the comparison of total -curvature with respect to -curvature (where ), specifically proving these results for metrics near strictly stable positive Einstein metrics and for negative Einstein metrics under specific sectional curvature assumptions.
This paper establishes that the inverse mean curvature flow by parallel hypersurfaces in space forms exists if and only if the initial hypersurface is isoparametric, providing explicit solutions and characterizing their long-term behavior and collapsing limits based on the number and multiplicity of principal curvatures.
This paper investigates Kähler manifolds that share locally isometric submanifolds, proving that a weak relative of a projective Kähler manifold is necessarily a strict relative, while also introducing and exemplifying the concept of strict relatives.
This paper extends PrvanoviÄ's coordinate-free formulation of the Einstein connection for almost Hermitian manifolds to almost contact metric manifolds satisfying an -torsion condition, providing explicit torsion formulas and analyzing special cases within the Gray-Hervella classification.
This paper generalizes Carrollian Lie algebroids to the framework of -commutative (almost commutative) geometry via -Lie-Rinehart pairs, establishing foundational analogues for Carrollian structures and demonstrating their application through explicit constructions on the extended quantum plane and the noncommutative 2-torus.
This paper investigates the blowup phenomena of Toda systems, which generalize the Liouville equation via simple Lie algebras, by providing concrete examples of blowup masses that correspond to Weyl groups.
This paper proposes that the patterns of spontaneous symmetry breaking and vacuum degeneracy in scalar and gauge field systems can be qualitatively classified by modeling the vacuum manifold as a principal groupoid bundle and analyzing the singular foliation it induces on the moduli space of vacuum expectation values.
This paper derives an explicit, non-asymptotic formula for the expected Lipschitz-Killing curvatures of excursion sets for arbitrary left-invariant Gaussian spin spherical random fields on with respect to an arbitrary metric, providing a general framework applicable to non-degenerate Gaussian fields on three-dimensional compact Riemannian manifolds for analyzing Cosmic Microwave Background polarization.
This paper establishes a relative Poincaré–Verdier duality for supermanifolds via Berezin fiber integration to rigorously define picture changing operators and prove the equivalence of component, superspace, and geometric formulations of 3d supergravity.
This paper demonstrates that stochastic gravitational wave memory from early universe and astrophysical sources exhibits a fractional Brownian motion scaling ( with ) that grows faster than standard Brownian motion, offering a distinct signature to extract these signals from PTA data and probe post-Big Bang conditions.