Abstract
AbstractIn this manuscript we study rotationally p-harmonic maps between spheres. We prove that for (p) given, there exist infinitely many p-harmonic self-maps of $$\mathbb {S}^m$$
S
m
for each $$m\in \mathbb {N}$$
m
∈
N
with $$p<m< 2+p+2\sqrt{p}$$
p
<
m
<
2
+
p
+
2
p
. In the case of the identity map of $$\mathbb {S}^m$$
S
m
we explicitly determine the spectrum of the corresponding Jacobi operator and show that for $$p>m$$
p
>
m
, the identity map of $$\mathbb {S}^m$$
S
m
is equivariantly stable when interpreted as a p-harmonic self-map of $$\mathbb {S}^m$$
S
m
.
Funder
Austrian Science Fund
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference20 articles.
1. Abramowitz, M, Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Volume 55 of National Bureau of Standards Applied Mathematics Series. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC (1964)
2. Baird, P., Gudmundsson, S.: $$p$$-harmonic maps and minimal submanifolds. Math. Ann. 294(4), 611–624 (1992)
3. Bizoń, P., Chmaj, T.: Harmonic maps between spheres. Proc. R. Soc. Lond. Ser. A 453(1957), 403–415 (1997)
4. Branding, V., Siffert, A.: On the equivariant stability of harmonic self-maps of cohomogeneity one manifolds. J. Math. Anal. Appl. 517(2), 126635 (2023)
5. Dong, Y., Lin, H.: Gradient estimate and Liouville theorems for $$p$$-harmonic maps. J. Geom. Anal. 31(8), 8318–8333 (2021)