Surfaces with boundary: their uniformizations, determinants of Laplacians, and isospectrality

Let \Sigma be a compact surface of type (g, n), n > 0, obtained by removing n disjoint disks from a closed surface of genus g. Assuming \chi(\Sigma)<0, we show that on \Sigma, the set of flat metrics which have the same Laplacian spectrum of Dirichlet boundary condition is compact in the C^\infty topology. This isospectral compactness extends the result of Osgood, Phillips, and Sarnak \cite{OPS3} for type (0,n) surfaces, whose examples include bounded plane domains. Our main ingredients are as following. We first show that the determinant of the Laplacian is a proper function on the moduli space of geodesically bordered hyperbolic metrics on \Sigma. Secondly, we show that the space of such metrics is homeomorphic (in the C^\infty-topology) to the space of flat metrics (on \Sigma) with constantly curved boundary. Because of this, we next reduce the complicated degenerations of flat metrics to the simpler and well-known degenerations of hyperbolic metrics, and we show that determinants of Laplacians of flat metrics on \Sigma, with fixed area and boundary of constant geodesic curvature, give a proper function on the corresponding moduli space. This is interesting because Khuri \cite{Kh} showed that if the boundary length (instead of the area) is fixed, the determinant is not a proper function when \Sigma is of type (g, n), g>0; while Osgood, Phillips, and Sarnak \cite{OPS3} showed the properness when g=0.Comment: Further Revised. A technical error is corrected; the sections devoted to the proof of the insertion lemma and the separation of variables method are completely rewritten. (Sections 4, 5, and 6 in this revised version.) A lot of changes, corrections, and improvements are made throughout the paper. No mathematical change in the main theorems listed in the introductio

Another look at yield spreads: Monetary policy and the term structure of interest rates

Liquidity plays an important role in explaining how banks determine their allocation of funds. This paper analyses whether this fact can explain the term structure of interest rates and yield spreads. The paper models banks' demand for liquidity in a manner similar to that used to study household need for liquidity, namely, by using a cash-in-advance type model. The paper finds that the shadow price of the cash-in-advance constraint plays an important role in determining yield spreads. The model predicts that short-term rates respond more to monetary policy than long-term rates, consistent with earlier empirical findings. The empirical part of the paper shows that the expectations hypothesis might be salvaged under the maintained hypothesis concerning the liquidity premium and default risk premium. This paper confirms the finding that monetary contractions raise nominal interest rates. --Term structure of interest rates,Expectations hypothesis,Yield Spreads,Liquidity,Cash-in-advance constraint,Monetary policy

The Effect of IT Innovation on Industrial Output Elasticities

Over the past decade, IT investment has been regarded as a key factor in enhancing productivity and economic development in Korea. This paper will assess whether the IT industry can positively affect structural change using an Input-Output model. Changes in Korean industries are traced using assumptions of IT innovation based on data from 1995 through 2000. Analysis reveals that the response of the economy falls short of our expectation that the development of the IT industry would generate growth in the productivity of the Korean economy. Government policy has been oriented toward cultivating IT industry through heavy investment, while neglecting efforts to make the overall industrial structure compatible with IT. We conclude that IT policy should be market-oriented to make the overall economy IT friendly so that industrial structures will respond more positively to IT developmentIT Industry, Output Elasticity, Productivity, Industrial Structure