134 papers
This survey article reviews the theory of twisted dynamical zeta functions of Ruelle and Selberg and explores Fried's conjecture, drawing from a mini-course delivered at the Institut Henri Poincaré.
This paper establishes that the number of quasi-Fuchsian surface subgroups in finite-volume noncompact hyperbolic 3-manifolds grows asymptotically as , a result that implies a similar lower bound for purely pseudo-Anosov surface subgroups in mapping class groups, while also demonstrating the existence of infinitely many conjugacy classes of surface subgroups with accidental parabolics.
This paper establishes that for certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, the potential -convergence of the corresponding collapsing Ricci-flat Kähler metrics can be improved to metric convergence on a generic region.
This paper establishes the well-posedness and -based Sobolev regularity for vector-valued fluid dynamics PDEs, including Stokes and Navier–Stokes equations, on closed manifolds of minimal regularity by developing a parametrization-free variational approach that decouples velocity and pressure variables.
This paper establishes necessary and sufficient cohomological conditions for representing classes by Real embedded surfaces in 4-manifolds and derives two versions of an adjunction inequality for their genus when Real Seiberg-Witten invariants are non-zero, demonstrating that the minimal genus for Real surfaces can exceed that of arbitrary embedded surfaces.
This paper extends C. Riehm's 1984 results on Riemannian -type Lie groups to the pseudo-Riemannian setting by providing a complete characterization of the geodesic orbit property for 2-step nilpotent Lie groups constructed from admissible Clifford modules of minimal dimension.
This paper classifies and constructs differential symmetry breaking operators from a line bundle over to a vector bundle over , while determining their factorization identities, the associated branching laws for generalized Verma modules of , and the resulting -representations.
This paper employs an information-theoretic approach to establish the equivalence between the curvature-dimension condition and entropy differential inequalities on Riemannian manifolds, while deriving new rigidity theorems for -Einstein and -Einstein manifolds through the monotonicity of -entropy along Wasserstein geodesics.
This paper introduces a complex of cochains known as -fractional charges to define the exterior product of Hölder differential forms, thereby extending the Young integral to arbitrary dimensions and codimensions.
This paper solves the Dirichlet problem for minimal Killing graphs over non-compact domains in 3-manifolds fibered by a Killing vector field, establishing Collin-Krust type estimates, proving uniqueness results in the Heisenberg group, and demonstrating the removability of isolated singularities.
This paper establishes the nonlinear stability of multi-dimensional rarefaction waves for the compressible Euler equations by introducing a novel Geometric Weighted Energy Method that overcomes derivative loss issues through the identification of a hidden vanishing structure in the top-order derivatives of the characteristic speed.
This paper establishes the Drinfeld correspondence between Poisson Lie groups and Lie bialgebras in the infinite-dimensional setting, specifically extending the theory to regular Lie groups modeled on convenient vector spaces such as nuclear Fréchet and Silva spaces, with applications to loop groups and diffeomorphism groups.
This paper investigates the Rumin differentials within irreducible unitary representations of the (2,3,5) nilpotent Lie group, computing their spectra and zeta-regularized determinants for Schrödinger representations while evaluating the analytic torsion for generic representations.
This paper introduces the extrinsic bi-conformal heat flow for biharmonic maps on 4-manifolds and proves that this flow exists globally and remains smooth without developing finite-time singularities.
This paper establishes that geodesic disks are the unique domains maximizing the first non-trivial Neumann eigenvalue among all simply connected regions of the sphere with a fixed area.
This paper develops a non-abelian, gauge-theoretic framework for the Schwarzian derivative and second-order differential equations on Riemann surfaces, applying it to generalize Dedekind's approach to higher-genus curves via matrix-valued equations on the Hodge bundle, analyze periods of cubic threefolds, and model mechanical mass-spring systems.
This paper constructs a principal twistor model for a crepant resolution of a conical symplectic variety and proves its universality in recovering asymptotic hyperkähler metrics, thereby establishing an inclusion of the corresponding moduli space into a finite-dimensional real vector space.
This paper establishes topological and rigidity results for four-dimensional hypersurfaces in five-dimensional space forms by characterizing isoparametric hypersurfaces via the Weyl tensor, deriving sharp bounds on the Weyl functional, estimating the second fundamental form in terms of the Euler characteristic, and proving rigidity through integral inequalities, with extensions to locally conformally flat ambient spaces.
The paper establishes that the number of compact, essential, orientable, non-isotopic surfaces with a fixed Euler characteristic embedded in a finite-volume hyperbolic 3-manifold is bounded by a polynomial function of the manifold's volume, where the degree of the polynomial depends linearly on the absolute value of the Euler characteristic.
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.