Manuscripta Mathematica最新文献

For n-dimensional weighted Riemannian manifolds, lower m-Bakry–Émery–Ricci curvature bounds with ({varepsilon })-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10(1):1–30, 2022), integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower m-Bakry–Émery–Ricci curvature bounds with ({varepsilon })-range. These generalize those inequalities under constant curvature bounds for (m in (n,infty )) to (min (-infty ,1]cup {infty }).

We classify isometric immersions (f:M^{n}rightarrow mathbb {R}^{n+p}), (n ge 5) and (2p le n), with constant Moebius curvature and flat normal bundle.

For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.

We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.

We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer–Manin obstruction vanishes, then apply results of Colliot-Thélène, Sansuc, and Swinnerton-Dyer.

In this note, we derive a Yau type gradient estimate for positive exponentially harmonic functions on Riemannian manifolds with compact boundary. As its application, we obtain a Liouville type theorem.

This paper focuses on Gromov hyperbolic characterizations of unbounded uniform domains. Let (Gsubsetneq mathbb {R}^n) be an unbounded domain. We prove that the following conditions are quantitatively equivalent: (1) G is uniform; (2) G is Gromov hyperbolic with respect to the quasihyperbolic metric and linearly locally connected; (3) G is Gromov hyperbolic with respect to the quasihyperbolic metric and there exists a naturally quasisymmetric correspondence between its Euclidean boundary and the punctured Gromov boundary equipped with a Hamenstädt metric (defined by using a Busemann function). As an application, we investigate the boundary quasisymmetric extensions of quasiconformal mappings, and of more generally rough quasi-isometries between unbounded domains with respect to the quasihyperbolic metrics.

We study a one-dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio–Baradat–Brenier, of the discrete Monge–Ampère gravitational model, which describes the motion of interacting particles whose dynamics is ruled by the optimal transport problem. The more general action-type functional we consider contains a discontinuous potential term related to the descending slope of the opposite squared distance function from a generic discrete set in (mathbb {R}^{d}). We exploit the underlying geometrical structure provided by the associated Voronoi decomposition of the space to obtain (C^{1,1})-regularity for local minimizers out of a finite number of shock times.

We give an alternative computation of the Betti and Hodge numbers for manifolds of OG6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.

Let ({mathfrak g}) be a reductive Lie algebra and (mathfrak tsubset mathfrak g) a Cartan subalgebra. The (mathfrak t)-stable decomposition ({mathfrak g}=mathfrak toplus {mathfrak m}) yields a bi-grading of the symmetric algebra ({mathcal {S}}({mathfrak g})). The subalgebra ({mathcal {Z}}_{({mathfrak g},mathfrak t)}) generated by the bi-homogenous components of the symmetric invariants (Fin {mathcal {S}}({mathfrak g})^{mathfrak g}) is known to be Poisson commutative. Furthermore the algebra ({tilde{{mathcal {Z}}}}=textsf{alg}langle {mathcal {Z}}_{({mathfrak g},{mathfrak t})},{mathfrak t}rangle ) is also Poisson commutative. We investigate relations between ({tilde{{mathcal {Z}}}}) and Mishchenko–Fomenko subalgebras. In type A, we construct a quantisation of ({tilde{{mathcal {Z}}}}) making use of quantum Mishchenko–Fomenko algebras.