RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.

Development of a global inundation map at high spatial resolution from topographic downscaling of coarse-scale remote sensing data

Large-scale estimates of the area of terrestrial surface waters have greatly improved over time, in particular through the development of multi-satellite methodologies, but the generally coarse spatial resolution (tens of kms) of global observations is still inadequate for many ecological applications. The goal of this study is to introduce a new, globally applicable downscaling method and to demonstrate its applicability to derive fine resolution results from coarse global inundation estimates. The downscaling procedure predicts the location of surface water cover with an inundation probability map that was generated by bagged derision trees using globally available topographic and hydrographic information from the SRTM-derived HydroSHEDS database and trained on the wetland extent of the GLC2000 global land cover map. We applied the downscaling technique to the Global Inundation Extent from Multi-Satellites (GIEMS) dataset to produce a new high-resolution inundation map at a pixel size of 15 arc-seconds, termed GIEMS-D15. GIEMS-D15 represents three states of land surface inundation extents: mean annual minimum (total area, 6.5 x 10(6) km(2)), mean annual maximum (12.1 x 10(6) km(2)), and long-term maximum (173 x 10(6) km(2)); the latter depicts the largest surface water area of any global map to date. While the accuracy of GIEMS-D15 reflects distribution errors introduced by the downscaling process as well as errors from the original satellite estimates, overall accuracy is good yet spatially variable. A comparison against regional wetland cover maps generated by independent observations shows that the results adequately represent large floodplains and wetlands. GIEMS-D15 offers a higher resolution delineation of inundated areas than previously available for the assessment of global freshwater resources and the study of large floodplain and wetland ecosystems. The technique of applying inundation probabilities also allows for coupling with coarse-scale hydro-climatological model simulations. (C) 2014 Elsevier Inc All rights reserved.