Skip to content

Commit

Permalink
Changes on web
Browse files Browse the repository at this point in the history
  • Loading branch information
jirilebl committed Jun 3, 2024
1 parent 679fa83 commit 332922e
Showing 1 changed file with 0 additions and 43 deletions.
43 changes: 0 additions & 43 deletions CHANGES
Original file line number Diff line number Diff line change
@@ -1,45 +1,2 @@
<li>Instead of the functional notation for plugging vectors into
differential forms, use the angle bracket pairing notation that is more
standard and since we don't really use this much at all, there is no reason to
have a less standard notation. This affects one place in chapter 1,
exercise 4.4.3, and one place in appendix C.
<li>The notation
\(\C \otimes T_p M\) is changed to the more
common \(\C T_p M\) which also avoids a slight abuse of notation.
Thanks to Richard Lärkäng for the suggestion.
<li>Lemma 2.3.9, the statement about the Levi form doesn't really make sense
if \(M\) is not a boundary, so change the statement to explicitly say that
the inside is "above" the \(M\) in the new coordinates.
Also explicitly mention this at the end of the proof.
Thanks to Richard Lärkäng for the suggestion.
<li>At the beginning of section 2.4, give a reference to the one-variable
book as not every student may have had a treatment of harmonic and
subharmonic functions in a one-variable course.
<li>Add hints to Exercise 2.4.8.
<li>Change Proposition 2.4.5, to be about the sub-mean-value property
for all small enough discs (which is really the best way to prove
the original statement in the first place),
leaving the original statement as an "In particular".
That also
<b>changes Exercise 2.4.11</b> by really making it a bit easier as it
gives a way to do it (and change the hint to that exercise too).
Thanks to Richard Lärkäng for the suggestion.
<li>In Example 2.5.4, put a square on the norm of \(z\) as that makes the
computation easier.
Thanks to Richard Lärkäng for the suggestion.
<li>In Theorem 2.5.6, add part (iv) which is just the conclusion of the
second version of the Kontinuitatssatz as that just follows from the proof
directly with no extra work.
Thanks to Richard Lärkäng for the suggestion.
<li>In Theorem 2.5.6, make part (ii) less wordy: "U is Hartogs
pseudoconvex". I mean the definition is just above the theorem!
<li>Mark Exercise 2.6.1 as Oka's lemma to make the connection to the "proof"
above clear.
<li><b>Change Exercise 4.4.1</b> to ask also to prove the Leibniz rule
(which easily follows from the first part and the real Leibniz rule), but
this is good to understand for the computations later in the section.
Thanks to Richard Lärkäng for the suggestion.
<li>Add Leibniz rule to Appendix C.
<li>Simplify the wording of some of the theorems in Appendix E.

See https://www.jirka.org/scv/changes.html for older changes.

0 comments on commit 332922e

Please sign in to comment.