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Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents 认领 引用
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作者 HWANG JunMuk 《Science China Mathematics》 SCIE CSCD 2015年第3期513-518,共6页
A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected... A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument. 展开更多
关键词 varieties of minimal rational tangents extension of holomorphic maps
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Exploring the correlation between spatial heterogeneity of urban tourism and the degree of crowd gathering: Take the main area of Wuhan, China as an example 认领 引用
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作者 Xincan Yu Hong Xu Yuelin Yan 《Frontiers of Architectural Research》 EI CSCD 2025年第5期1328-1349,共22页
Urban tourism space is the primary area where tourism activities occur and a key driver of regional tourism space evolution.To explore the correlation between population aggregation and urban tourism spatial heterogen... Urban tourism space is the primary area where tourism activities occur and a key driver of regional tourism space evolution.To explore the correlation between population aggregation and urban tourism spatial heterogeneity in the big data era,this study focuses on Wuhan’s main urban area in 2023.Using the Geographically Weighted Regression model,it analyzes the factors influencing tourism spatial heterogeneity.Additionally,Baidu Heat map data is employed to identify crowd aggregation levels during holidays,revealing the distribution patterns of urban tourism space.The results indicate that(1)factors derived from the GWR model significantly influence the number of tourism spaces in Wuhan,with evident spatial differences;(2)based on the spatial matching of heterogeneity factors and crowd aggregation levels,urban tourism space can be categorized into six types,including five core tourism spaces and other scattered spaces.This research highlights the spatial heterogeneity of urban tourism in Wuhan and provides a scientific basis for the transformation and quality improvement of urban tourism space by exploring the impact of population activity density. 展开更多
关键词 Tourism space Correlation study Spatial heterogeneity GWR model Heat map on Baidu map Extension
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