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.

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.