On nn-superharmonic functions and some geometric applications

In this paper we study asymptotic behavior of $n$-superharmonic functions at isolated singularity using the Wolff potential and $n$-capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of Arsove-Huber and Taliaferro in 2 dimensions. To study $n$-superharmonic functions we use a new notion of $n$-thinness by $n$-capacity motivated by a type of Wiener criterion in Arsove-Huber's paper. To extend Taliaferro's work, we employ the Adams-Moser-Trudinger inequality for the Wolff potential, which is inspired by the one used by Brezis-Merle. For geometric applications, we study the asymptotic end behavior of complete conformally flat manifolds as well as complete properly embedded hypersurfaces in hyperbolic space. In both geometric applications the strong $n$-capacity lower bound estimate of Gehring in 1961 is brilliantly used. These geometric applications seem to elevate the importance of $n$-Laplace equations and make a closer tie to the classic analysis developed in conformal geometry in general dimensions.Comment: 46 page

Hypersurfaces with nonnegative Ricci curvature in hyperbolic space

Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier in 1990.Comment: 14 page

Political connection, founder-manager and their impact on tunneling in China\u27s listed firms

Reciprocal relationship, often regarded as mutually beneficial and secure, can actually be destructive and result in inefficiency. We provide evidence of such double-blade by studying the impact of political connection on corporate governance. Private firms in countries where the government controls the allocation of resources have incentives to seek political connections by hiring politicians or ex-politicians as top executives. Such political capital, however, may turn into political constraint when the CEOs fail to perform but use connections to entrench themselves. We take advantage of the unique setting in China to illustrate this argument. We show that politically connected CEOs have significantly weaker performance, longer tenure, lower turnover, and lower turnover-performance sensitivity than non-politically connected CEOs in China\u27s privately controlled firms. Firm performance improvement is also less following forced turnover of the former than the latter. These entrenchment effects are alleviated in firms that are politically secured through alternative connection channels. The overall results suggest that political capital often turns into political constraints causing sizable inefficiency in Chinese private firms

Earnings quality and stress levels of Chinese listed companies

This paper investigates the relation between earnings quality and stress levels of Chinese companies listed in Shanghai and Shenzhen stock exchanges from 2003 to 2007 by classifying them as financially stressed and bankrupt (SB), financially stressed and not bankrupt (SNB), and not financially stressed and not bankrupt (NSNB) firms. We measure the earnings quality by four separate attributes: accruals quality, earnings persistence, earnings predictability, and earnings smoothness. We find that earnings quality levels are parallel to firm\u27s stress levels: the SB firms have the lowest earnings quality measured by each of the four earnings attributes, the SNB firms have a lower earnings quality compared with the SB firms, the NSNB firms have the highest earnings quality. We also find that the earnings quality deteriorated over the study period, the number of SB firms with the lowest earnings quality increased, and the number of NSNB firms with the highest earnings quality decreased for the fiscal years 2003 to 2007