1,721,247 research outputs found
Sub-Finsler geometry and finite propagation speed
No full textWe prove a number of results on the geometry associated to the solutions of first-order differential operators on manifolds. In particular, we consider distance functions associated to a first-order operator, and discuss the associated geometry, which is sometimes surprisingly different to Riemannian geometry
The price of a disadvantaged location: Regional variation in the price and supply of short-term credit to SMEs in UK
No full textAccess to inexpensive short-term credit from banks is vital for many small and medium enterprises (SMEs), which face liquidity problems because of an imbalance between cash outflows and receipt of outstanding payments. This article investigates the key determinants of short-term credit access and pricing for UK SMEs, disentangling between regional effects and firm-specific effects (that is, credit risk ratings). We use a large dataset of 30,183 responses to six waves of the SME Finance Monitor survey. While there are underlying differences at the firm level in risk behavior across regions, our key finding is that, faced with the same risk, banks do react fairly to funding applications in terms of access but not price at the regional level. We conclude that regional differences directly and indirectly affect the way banks allocate and price short-term credit. There is evidence of a peripheral region price penalty
Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III
No full textThis paper is the third of a series on semigroups of operator related to the Laplace Beltrami operator on a symmetric space of the non compact type. We consider the Poisson semigroup P_{τ,θ}, when θ=1 and τ is complex and Reτ>0. We remark that the shifted Laplace Beltrami operator -L+b, corresponding to the case θ=1, occurs naturally in geometry, as it is conformally invariant.
Our main theorem describes the behaviour of the Lp-Lq operator norm of P_{τ,1} for various possible values of p and q and for τ in various subsets of the right half of the complex plane. This description is nearly complete, but when p<2<q and |τ| is large but τ is nearly imaginary, our methods do not yield good estimates
The Cayley transform and uniformly bounded representations
No full textLet G be a simple Lie group of real rank one, with Iwasawa decomposition KA \bar N and Bruhat
big cell NMA\bar N: Then the space G/MA \bar N may be (almost) identified with N and with K /M,
and these identifications induce the (generalised) Cayley transform C : N \to K /M. We show
that C is a conformal map of Carnot–Caratheodory manifolds, and that composition with the
Cayley transform, combined with multiplication by appropriate powers of the Jacobian,
induces isomorphisms of Sobolev spaces on N
and on K/M. We use this to construct
uniformly bounded and slowly growing representations of G
Can Small Firms Innovate Away From Competition?
Full text linkIn this paper we test whether innovation allows entrepreneurs to navigate their way out of highly competitive markets into calmer waters where competitive pressures are reduced. In doing so, we establish three key findings: first, in line with the Schumpeterian creative destruction theory, our results document a decreasing marginal effect of prior innovation on consecutive perceived competition, an effect that is stronger for small firms operating in more competitive markets; then, we highlight the different synergistic effects generated by the complementarity between tangible and intangible innovation activities in competitive and oligopolistic markets that support the Schumpeterian view; finally, we establish that such synergies have proven crucial in navigating out of the COVID-19 pandemic
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