f-Harmonic Maps Within Bounded Distance from Quasi-isometric Maps

Qun Chen , Kaipeng Li , Hongbing Qiu

Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 815 -825.

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Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 815 -825. DOI: 10.1007/s40304-021-00276-1
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f-Harmonic Maps Within Bounded Distance from Quasi-isometric Maps

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Abstract

In this article, we prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from an f-harmonic map.

Keywords

F-harmonic map / Quasi-isometric map / Rank one symmetric spaces

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Qun Chen, Kaipeng Li, Hongbing Qiu. f-Harmonic Maps Within Bounded Distance from Quasi-isometric Maps. Communications in Mathematics and Statistics, 2023, 11(4): 815-825 DOI:10.1007/s40304-021-00276-1

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References

[1]

Benoist Y, Hulin D. Harmonic quasi-isometric maps between rank one symmetric spaces. Ann. Math.. 2017, 185 3 895-917

[2]

Bonsante F, Schlenker M. Maximal surfaces and the universal Teichmuller space. Invent. Math.. 2010, 182 279-333

[3]

Calabi, E.: An extension of E. Hopf’s maximum principle with an application to Riemannian geometry. Duke Math. J. 25, 45–56 (1958)

[4]

Chen Q, Jost J, Qiu H-B. Existence and Liouville theorems for V -harmonic maps from complete manifolds. Ann. Global Anal. Geom.. 2012, 42 4 565-584

[5]

Chen Q, Jost J, Wang G-F. A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry. J. Geom. Anal.. 2015, 25 4 2407-2426

[6]

Chen Q, Qiu H-B. Rigidity of self-shrinkers and translating solitons of mean curvature flows. Adv. Math.. 2016, 294 517-531

[7]

Cheng, S.Y.: Liouville theorem for harmonic maps, geometry of the Laplace operator. In: Proceedings of the Symposium in Pure Mathematics. University of Hawaii, Honolulu, Hawaii, 1979, pp. 147–151, Proceedings of the Symposium in Pure Mathematics, XXXVI, American Mathematical Society, Provi- dence, RI (1980)

[8]

Eells J, Lemaire L. A report on harmonic maps. Bull. London Math. Soc.. 1978, 10 1 1-68

[9]

Hardt R, Wolf M. Harmonic extensions of quasiconformal maps to hyperbolic space. Indiana Univ. Math. J.. 1997, 46 155-163

[10]

Lemm, M., Markovic, V.: Heat flows on hyperbolic spaces. arXiv:1506.04345 (2015)

[11]

Li P, Wang J. Harmonic rough isometries into Hadamard space. Asian J. Math.. 1998, 2 419-442

[12]

Lichnerowicz A. Applications harmoniques et variétés kähleriennes. Symp. Math.. 1969, 3 341-402

[13]

Markovic V. Harmonic diffeomorphisms of noncompact surfaces and Teichmuller spaces. J. London Math. Soc.. 2002, 65 103-114

[14]

Markovic V. Harmonic maps between 3-dimensional hyperbolic spaces. Invent. Math.. 2015, 199 921-951

[15]

Schoen, R.: The role of harmonic mappings in rigidity and deformation problems. Complex geometry(Osaka, 1990), Lecture Notes in Pure and Applied Mathematics 143, 179-200, Dekker, New York (1993)

[16]

Schoen, R., Yau, S.-T.: Complete three dimensional manifolds with positive Ricci curvature and scalarcurvature, Seminaron Differential Geometry(Yau, S.T. ed.). Ann. of Math. Stud. 102, 209–228 (1982)

[17]

Simon, L.: Theorems on regularity and singularity of energy minimizing maps. Lecture Notes in Mathematics. ETH Zurich, Birkhaüser (1996)

[18]

Shen Y. A Liouville theorem for harmonic maps. Am. J. Math.. 1995, 117 3 773-785

[19]

Tam L-F, Wan T. Quasi-conformal harmonic diffeomorphism and the universal Teichmüller space. J. Diff. Geom.. 1995, 42 368-410

Funding

national natural science foundation of china(11571259)

Fundamental Research Funds for the Central Universities (CN)(2042019kf0198)

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