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Diffusion semigroup on manifolds with time-dependent metrics Cheng, Li Juan in Forum Mathematicum (2017), 29(4), 751-1002 Let $L_t:=\Delta_t +Z_t $, $t\in [0,T_c)$ on a differential manifold equipped with a complete geometric flow $(g_t)_{t\in [0,T_c)}$, where $\Delta_t$ is the Laplacian operator induced by the metric $g_t ... [more ▼] Let $L_t:=\Delta_t +Z_t $, $t\in [0,T_c)$ on a differential manifold equipped with a complete geometric flow $(g_t)_{t\in [0,T_c)}$, where $\Delta_t$ is the Laplacian operator induced by the metric $g_t$ and $(Z_t)_{t\in [0,T_c)}$ is a family of $C^{1,\infty}$-vector fields. In this article, we present a number of equivalent inequalities for the lower bound curvature condition, which include gradient inequalities, transportation-cost inequalities, Harnack inequalities and other functional inequalities for the semigroup associated with diffusion processes generated by $L_t$. To this end, we establish the derivative formula for the associated semigroup and construct couplings for these diffusion processes by parallel displacement and reflection. [less ▲] Detailed reference viewed: 275 (66 UL)Brackets with (τ, σ )-derivations and (p, q)-deformations of Witt and Virasoro algebras Elchinger, Olivier ; ; et al in Forum Mathematicum (2015) The aim of this paper is to study some brackets defined on (τ, σ )-derivations sat- isfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well ... [more ▼] The aim of this paper is to study some brackets defined on (τ, σ )-derivations sat- isfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions gen- eralize the results obtained by Hartwig, Larsson and Silvestrov on σ -derivations, arising in connection with discretizations and deformations of algebras of vector fields. [less ▲] Detailed reference viewed: 158 (13 UL)An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module Schlichenmaier, Martin in Forum Mathematicum (2014), 26(3), 913-929 By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields ... [more ▼] By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these algebras. The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpublished note. It is based on cumbersome calculations. Compared to the original proof the presented one is quite elegant and considerably simpler. [less ▲] Detailed reference viewed: 162 (14 UL)Large torsion subgroups of split Jacobians of curves of genus two or three ; Leprévost, Franck ; in Forum Mathematicum (2000), 12 Detailed reference viewed: 98 (0 UL) |
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