A second Ph.D. in mathematics?

With enough motivation, you can learn new areas and go there. I started my first two papers in complex analysis, related to the Schrodinger equation. I am now doing algebraic combinatorics related to representation theory, some quasi-symmetric functions and enumerative aspects of combinatorics. On the side, I have also worked a bit on polytopes, and an unfinished project which are related to invariant measures and Julia fractals.

There is no point of taking a second PhD - having a PhD means you should be mature enough to read research articles and study mathematics by yourself without having to take classes. You are also (I hope) familiar with the ethical aspects of research and the submission/review process. You should also know what constitutes a well-written paper and you are now familiar with LaTeX and mathematical software and how to present mathematics in form of posters and talks.

Finish this degree, then switch to whatever interests you. Many (most?) mathematicians change fields at some point in their research careers.

Bob Solovay told me once that the most important research was the first new thing you did after you got your degree. His thesis was A Functorial Form of the Differentiable Riemann–Roch theorem. He finished it in a hurry so he could move on to mathematical logic, where he's famous.

https://en.wikipedia.org/wiki/Robert_M._Solovay

I understand the OP is frustrated with tight job market and those are valid concerns, but his/her description of the geometric analysis as a shallow subject is ridiculous. Parts of geometric analysis certainly attract top people and have seen remarkable recent progress. How a new Ph.D. could fail to notice these happenings is a mystery.

@ZhiqiangSun: Now that you have a Ph.D. you are free to tackle "nontrivial and natural problems". There are plenty of those in geometric analysis, and as to whether the subject involves any "beautiful ideas", it is my opinion that it surely does. If some papers seem shallow, ignore them. Based on your stated background you might enjoy working on degenerations of Kaehler metrics, which involves a healthy mix of geometric PDE (eg Kaehler-Ricci flow) and algebraic/complex geometry. You may wish to start by reading recent works of Simon Donaldson and Gang Tian.

It is common for mathematicians to change their research area several times during their career. Doing so after the PhD is quite possible, but it could be risky careerwise. It may be best to proceed slowly and expand to adjacent areas. Moving between two subfield of geometric analysis is not really a big change and many people do so.