From 2a11f6e656a78445ea8a1b96ade83402781f33f5 Mon Sep 17 00:00:00 2001 From: Luke Naylor <l.naylor@sms.ed.ac.uk> Date: Tue, 11 Apr 2023 14:55:19 +0100 Subject: [PATCH] Mention B.Schmidt and algorithm --- main.tex | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/main.tex b/main.tex index 727da0b..f738229 100644 --- a/main.tex +++ b/main.tex @@ -56,6 +56,16 @@ $0 \leq \chern^\beta_1(E) \leq \chern^\beta_1(F)$. Finally, there's a condition ensuring that the radius of the circular wall is strictly positive: $\chern^\beta_2(E) > 0$. +For any fixed $\chern_0(E)$, the inequality +$0 \leq \chern^{\beta_{-}}_1(E) \leq \chern^{\beta_{-}}_1(F)$, +allows us to bound $\chern_1(E)$. Then, the other inequalities allow us to +bound $\chern_2(E)$. The final part to showing the finiteness of pseudowalls +would be bounding $\chern_0(E)$. This has been hinted at in [ref] and done +explicitly by Benjamin Schmidt within a computer program which computes +pseudowalls. Here we discuss these bounds in more detail, along with the methods +used, followed by refinements on them which give explicit formulae for tighter +bounds on $\chern_0(E)$ of potential destabilizers $E$ of $F$. + \section{Section 1} -- GitLab