Browse > Article
http://dx.doi.org/10.4134/BKMS.b210351

ON VANISHING THEOREMS FOR LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS  

Nguyen, Dang Tuyen (Department of Mathematics National University of Civil Engineering)
Pham, Duc Thoan (Department of Mathematics National University of Civil Engineering)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.2, 2022 , pp. 469-479 More about this Journal
Abstract
In this paper, we obtain some vanishing theorems for p-harmonic 1-forms on locally conformally flat Riemannian manifolds which admit an integral pinching condition on the curvature operators.
Keywords
p-Harmonic 1-form; vanishing theorems; locally conformally flat;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. Schoen and S.-T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), no. 1, 47-71. https://doi.org/10.1007/BF01393992   DOI
2 P. Li and J. Wang, Weighted Poincare inequality and rigidity of complete manifolds, Ann. Sci. Ecole Norm. Sup. (4) 39 (2006), no. 6, 921-982. https://doi.org/10.1016/j.ansens.2006.11.001   DOI
3 N. T. Dung and K. Seo, p-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold, Ann. Mat. Pura Appl. (4) 196 (2017), no. 4, 1489-1511. https://doi.org/10.1007/s10231-016-0625-0   DOI
4 P. Li and L.-F. Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geom. 35 (1992), no. 2, 359-383. http://doi.org/10.4310/jdg/1214448079   DOI
5 F. Duzaar and M. Fuchs, On removable singularities of p-harmonic maps, Ann. Inst. H. Poincare Anal. Non Lineaire 7 (1990), no. 5, 385-405. https://doi.org/10.1016/S0294-1449(16)30283-9   DOI
6 Y. Han and H. Pan, Lp p-harmonic 1-forms on submanifolds in a Hadamard manifold, J. Geom. Phys. 107 (2016), 79-91. https://doi.org/10.1016/j.geomphys.2016.05.006   DOI
7 K.-H. Lam, Results on a weighted Poincare inequality of complete manifolds, Trans. Amer. Math. Soc. 362 (2010), no. 10, 5043-5062. https://doi.org/10.1090/S0002-9947-10-04894-4   DOI
8 H. Lin, On the structure of conformally flat Riemannian manifolds, Nonlinear Anal. 123/124 (2015), 115-125. https://doi.org/10.1016/j.na.2015.05.001   DOI
9 N. Nakauchi, A Liouville type theorem for p-harmonic maps, Osaka J. Math. 35 (1998), no. 2, 303-312. http://projecteuclid.org/euclid.ojm/1200788071
10 M. Vieira, Vanishing theorems for L2 harmonic forms on complete Riemannian manifolds, Geom. Dedicata 184 (2016), 175-191. https://doi.org/10.1007/s10711-016-0165-1   DOI
11 X. Zhang, A note on p-harmonic 1-forms on complete manifolds, Canad. Math. Bull. 44 (2001), no. 3, 376-384. https://doi.org/10.4153/CMB-2001-038-2   DOI
12 Y. Han, Q. Zhang, and M. Liang, Lp p-harmonic 1-forms on locally conformally flat Riemannian manifolds, Kodai Math. J. 40 (2017), no. 3, 518-536. https://doi.org/10.2996/kmj/1509415230   DOI
13 H.-D. Cao, Y. Shen, and S. Zhu, The structure of stable minimal hypersurfaces in ℝn+1, Math. Res. Lett. 4 (1997), no. 5, 637-644. https://doi.org/10.4310/MRL.1997.v4.n5.a2   DOI
14 L.-C. Chang, C.-L. Guo, and C.-J. A. Sung, p-harmonic 1-forms on complete manifolds, Arch. Math. (Basel) 94 (2010), no. 2, 183-192. https://doi.org/10.1007/s00013-009-0079-3   DOI
15 J.-T. R. Chen and C.-J. A. Sung, Harmonic forms on manifolds with weighted Poincare inequality, Pacific J. Math. 242 (2009), no. 2, 201-214. https://doi.org/10.2140/pjm.2009.242.201   DOI
16 N. T. Dung and C.-J. A. Sung, Analysis of weighted p-harmonic forms and applications, Internat. J. Math. 30 (2019), no. 11, 1950058, 35 pp. https://doi.org/10.1142/s0129167x19500587   DOI
17 N. T. Dung and C.-J. A. Sung, Manifolds with a weighted Poincare inequality, Proc. Amer. Math. Soc. 142 (2014), no. 5, 1783-1794. https://doi.org/10.1090/S0002-9939-2014-11971-X   DOI
18 N. T. Dung and P. T. Tien, Vanishing properties of p-harmonic ℓ-forms on Riemannian manifolds, J. Korean Math. Soc. 55 (2018), no. 5, 1103-1129. https://doi.org/10.4134/JKMS.j170575   DOI