$$\Phi $$-Harmonic Maps and $$\Phi $$-Superstrongly Unstable Manifolds
نویسندگان
چکیده
We motivate and define $$\Phi $$ -energy density, -energy, -harmonic maps stable maps. Whereas harmonic or p-harmonic can be viewed as critical points of the integral first symmetric function $$\sigma _1$$ a pull-back tensor, second _2$$ tensor. By an extrinsic average variational method in calculus variations [cf. Howard Wei (Trans Am Math Soc 294:319–331, 1986), Yau (J Geom Anal 4(2):247–272, 1994), (Indiana Univ J 47(2):625–670, 1998) (Contemp 646:127–167, 2015)], we derive variation formulas for functional, express them orthogonal notation terms differential matrix, find -superstrongly unstable $$(\Phi - $$\text {SSU})$$ manifolds. prove, particular that every compact {SSU}$$ manifold must -strongly {SU})$$ , i.e., (a) A cannot target any nonconstant from manifold, (b) The homotopic class map into contains elements arbitrarily small (c) domain (d) Theorem 1.1(a),(b),(c), (d).] provide many examples manifolds, which include but not limit to spheres some Yang-Mills fields Bourguignon et al. (Proc Natl Acad Sci 76(4):1550–1553, 1979), Lawson (Commun Phys 79(2):189–230, 1981), Kobayashi (Math Z 193(2):165–189, 33(4):511–529, 1984) Wu (Br Comput 8(4):318–329, -harmonic, -unstable are constant. establish link -SSU p-SSU topology. variations, employed is contrast PDE applied Chen Symmetry 52:27–46, 2019) obtain sharp growth estimates warping functions multiply warped product
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2021
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-021-00770-6