Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (6): 2341-2360.doi: 10.1007/s10473-024-0616-y
Previous Articles Next Articles
Canhui LU, Xingdi CHEN†
Received:
2023-07-15
Revised:
2023-12-15
Published:
2024-12-06
Contact:
† Xingdi CHEN, E-mail: chxtt@hqu.edu.cn
About author:
Canhui LU, E-mail: lucanhui@stu.hqu.edu.cn
Supported by:
CLC Number:
Canhui LU, Xingdi CHEN. VALUE DISTRIBUTION PROPERTIES FOR GAUSS MAPS OF IMMERSED HARMONIC SURFACES RAMIFIED OVER HYPERSURFACES[J].Acta mathematica scientia,Series B, 2024, 44(6): 2341-2360.
[1] Ahlfors L V.An extension of Schwarz's lemma. Trans Amer Math Soc, 1938, 43: 359-364 [2] Aladro G, Krantz S G.A criterion for normality in ![]() [3] Alarcón A, López F J.On harmonic quasiconformal immersions of surfaces in ![]() [4] An D P, Quang S D, Thai D D.The second main theorem for meromorphic mappings into a complex projective space. Acta Math Vietnam, 2013, 38(1): 187-205 [5] Campana F, Winkelmann J.A Brody theorem for orbifolds. Manuscripta Math, 2009, 128(2): 195-212 [6] Chen X D, Li Y Z, Liu Z X, Ru M.Curvature estimate on an open Riemann surface with induced metric. Math Z, 2021, 298(1/2): 451-467 [7] Chen X D, Liu Z X, Ru M.Value distribution properties for the Gauss maps of the immersed harmonic surfaces. Pacific J Math, 2020, 309(2): 267-287 [8] Fujimoto H.Modified defect relations for the Gauss map of minimal surfaces. II. J Differential Geom, 1990, 31(2): 365-385 [9] Fujimoto H. On the number of exceptional values of the Gauss maps of minimal surfaces. J Math Soc Japan, 1988, ![]() ![]() [10] Fujimoto H.Value Distribution Theory the Gauss Map of Minimal Surfaces in ![]() [11] Ha P H.An estimate for the Gaussian curvature of minimal surfaces in ![]() [12] Jensen G R, Rigoli M.Harmonically immersed surfaces of ![]() [13] Kalaj D.The Gauss map of a hamonic surface. Indag Math (NS), 2013, 24(3): 415-427 [14] Kalaj D, Vujadinović D.Quasiconformal harmonic graphs. Complex Var Elliptic Equ, 2023, 68(8): 1407-1418 [15] Klotz T.Surfaces harmonically immersed in ![]() ![]() [16] Klotz T.A complete ![]() ![]() ![]() ![]() ![]() ![]() ![]() [17] Liu X J, Pang X C.Normal family theory and Gauss curvature estimate of minimal surfaces in ![]() [18] Liu Z X, Li Y Z, Chen X D. The value distribution of Gauss maps of immersed harmonic surfaces with ramification. Acta Math Sci, 2022, ![]() ![]() ![]() [19] Lu C H, Chen X D.Unicity theorem for generalized Gauss maps of immersed harmonic surfaces. J Math Anal Appl, 2023, 519: 126827 [20] Milnor T K.Are harmonically immersed surfaces at all like minimally immersed surfaces?// Seminar on Minimal Submanifolds. Princeton: Princeton University Press, 1983: 99-110 [21] Milnor T K.Harmonically immersed surfaces. J Differential Geom, 1979, 14(2): 205-214 [22] Milnor T K.Restrictions on the curvatures of ![]() [23] Osserman R, Ru M.An estimate for the Gauss curvature of minimal surfaces in ![]() [24] Quang S D.Curvature estimate and the ramification of the holomorphic maps over hypersurfaces on Riemann surfaces. Bull Soc Math France, 2023, 151(1): 91-115 [25] Quang S D.Modified defect relation of Gauss maps on annular ends of minimal surfaces for hypersurfaces of projective varieties in subgeneral position. J Math Anal Appl, 2024, 23(1): 127806 [26] Quang S D.Modified defect relation of Gauss maps of minimal surfaces for hypersurfaces of projective varieties in subgeneral position. arXiv:2107.08986 [27] Ru M.Gauss map of minimal surfaces with ramification. Trans Amer Math Soc, 1993, 339(2): 751-764 [28] Ru M.Nevanlinna Theory and Its Relation to Diophantine Approximation. Hackensack, NJ: World Scientific Publishing, 2021 [29] Ru M.On the Gauss map of minimal surfaces immersed in ![]() |
[1] | Thomas E. Cecil. CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY* [J]. Acta mathematica scientia,Series B, 2024, 44(1): 1-36. |
[2] | Huiyang XU, Cece LI. CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM* [J]. Acta mathematica scientia,Series B, 2023, 43(6): 2413-2429. |
[3] | Zizhou TANG, Wenjiao YAN. ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES [J]. Acta mathematica scientia,Series B, 2022, 42(6): 2223-2229. |
[4] | Jiaxing HUANG, Tuen Wai NG. A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES [J]. Acta mathematica scientia,Series B, 2022, 42(4): 1631-1644. |
[5] | Zhixue LIU, Yezhou LI, Xingdi CHEN. THE VALUE DISTRIBUTION OF GAUSS MAPS OF IMMERSED HARMONIC SURFACES WITH RAMIFICATION [J]. Acta mathematica scientia,Series B, 2022, 42(1): 172-186. |
[6] | Hongcun DENG. A BRAY-BRENDLE-NEVES TYPE INEQUALITY FOR A RIEMANNIAN MANIFOLD [J]. Acta mathematica scientia,Series B, 2021, 41(2): 487-492. |
[7] | Zhenlian LIN, Qingtian SHI. PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS [J]. Acta mathematica scientia,Series B, 2020, 40(6): 1874-1882. |
[8] | Wenjuan ZHANG, Jie FEI, Xiaoxiang JIAO. CLASSFICATION OF HOMOGENEOUS TWO-SPHERES IN G(2, 5; C) [J]. Acta mathematica scientia,Series B, 2019, 39(1): 312-328. |
[9] | Yi QI, Fei SONG. A NEW PROOF OF THE DELTA INEQUALITY [J]. Acta mathematica scientia,Series B, 2015, 35(5): 1137-1141. |
[10] | YANG Deng-Yun, XU Hong-Wei, FU Hai-Ping. NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES [J]. Acta mathematica scientia,Series B, 2013, 33(5): 1269-1274. |
[11] | Mohamed JLELI. STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE [J]. Acta mathematica scientia,Series B, 2013, 33(3): 830-838. |
[12] | SU Bian-Ping, SHU Shi-Chang, Yi Annie Han. HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE [J]. Acta mathematica scientia,Series B, 2011, 31(3): 1091-1102. |
[13] | JIAO Xiao-Xiang, PENG Jia-Gui. ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5) [J]. Acta mathematica scientia,Series B, 2011, 31(1): 237-248. |
[14] | CHEN Xu-Zhong, SHEN Yi-Bing. A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS [J]. Acta mathematica scientia,Series B, 2010, 30(4): 1053-1064. |
[15] | Chu Yuming; Cheng Jinfa; Wang Gendi. REMARKS ON JOHN DISKS [J]. Acta mathematica scientia,Series B, 2009, 29(1): 160-168. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
Full text 2
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Abstract 27
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|