Monotonicity Formulae and Holomorphicity of Harmonic Maps between K\"ahler manifolds

In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps into any Kaehler manifolds and harmonic maps into Kaehler manifolds with strongly semi-negative curvature respectively. These monotonicity inequalities enable us to derive some holomorphicity and Liouville type results for these pluriharmonic maps and harmonic maps. We also use the stress-energy tensors to investigate the holomorphic extension problem of CR maps.Comment: 46 page

A Bibliometrics Portrait of Chinese Research through the Lens of China Economic Review. A research proposal.

Notwithstanding, in the last two decades, there has been a noticeable increase in published work on the research field of Chinese economy. There are few studies, which analyze the evolution of Chinese economics research, and the weight of international economics within it, by resorting to objective methods, namely bibliometrics. Giving our focus on Chinese economics related research, we select to base our empirical analysis on the “seed journal” China Economic Review (CER), which is the most important economic journal especially concerned with the issues of Chinese economy. We classify and assess all the (522) articles that were published in CER from its genesis (1989) up to December 2010. We construct three main databases: the first database as bibliographic database that contains the more than 500 articles published in CER, where we classify articles by themes (such as Macroeconomics, Microeconomics and International Economics) and types(such as formal vs. empirical); the second database includes the references of those 500 articles, which we denominate ‘roots of Chinese economics research’; and the third database, the ‘influence of Chinese economics research’, where we have all the studies that cited (more than 3000 references) the 500 articles published in CER. By undertaking an exploratory statistical analysis on the three databases - bibliographic database, ‘roots’ database and ‘influence’ database, we are able to assess three main group of issues: 1) the importance, within Chinese economics of the topic ‘international economic’; the types of research that are pursued in the period of analysis (formal vs empirical); and the most prolific authors in the area; 2) the ‘roots’ of Chinese economics, that is, who and which outlets are influencing most Chinese economics research; 3) the scope of influence of Chinese economics literature.Evolution of research, Economics, Bibliometrics, China Economic Review