Abstract
We define a negative exponential harmonic map from the ball B{sup n} of R{sup n} into the sphere S{sup n} of R{sup n+1}. And we prove that the equator map u{sup *} = (x/x, 0) is a negative exponential harmonic map, but not stable for the negative exponential functional when n{>=}2. Moreover, if we consider maps from a ball B{sup n} into the unit sphere S{sup m} of R{sup m} where m{>=}2, we prove that no nonconstant map can reach either the minimum or the maximum of the negative exponential functional. (author). 19 refs.
Citation Formats
Minchun, Hong.
The equator map and the negative exponential functional.
IAEA: N. p.,
1991.
Web.
Minchun, Hong.
The equator map and the negative exponential functional.
IAEA.
Minchun, Hong.
1991.
"The equator map and the negative exponential functional."
IAEA.
@misc{etde_10105502,
title = {The equator map and the negative exponential functional}
author = {Minchun, Hong}
abstractNote = {We define a negative exponential harmonic map from the ball B{sup n} of R{sup n} into the sphere S{sup n} of R{sup n+1}. And we prove that the equator map u{sup *} = (x/x, 0) is a negative exponential harmonic map, but not stable for the negative exponential functional when n{>=}2. Moreover, if we consider maps from a ball B{sup n} into the unit sphere S{sup m} of R{sup m} where m{>=}2, we prove that no nonconstant map can reach either the minimum or the maximum of the negative exponential functional. (author). 19 refs.}
place = {IAEA}
year = {1991}
month = {Jun}
}
title = {The equator map and the negative exponential functional}
author = {Minchun, Hong}
abstractNote = {We define a negative exponential harmonic map from the ball B{sup n} of R{sup n} into the sphere S{sup n} of R{sup n+1}. And we prove that the equator map u{sup *} = (x/x, 0) is a negative exponential harmonic map, but not stable for the negative exponential functional when n{>=}2. Moreover, if we consider maps from a ball B{sup n} into the unit sphere S{sup m} of R{sup m} where m{>=}2, we prove that no nonconstant map can reach either the minimum or the maximum of the negative exponential functional. (author). 19 refs.}
place = {IAEA}
year = {1991}
month = {Jun}
}