November 2023
Intermediate to advanced
192 pages
3h 29m
English
We begin with Theorem 11.23.
Proof: Using the Lojasiewicz inequality, (see Chapter 8), there exists a Euclidean motion
for which we have
Without loss of generality, we may replace
by
. Hence, we may suppose that
Now we will employ a similar technique to the proof of Lemma 9.15.
Let
be a smooth cut off function on
such that
for
,
for and with for all . Then set
The summands are smooth and have pairwise disjoint supports ...