What to do if a co-author is delaying announcement of results?
I think you should push harder to get the paper onto arXiv. The important thing is to have a rational discussion with your co-author where you discuss your worries and try to address them. Here are some additional arguments you can try to use to convince your co-author:


If someone discovered your main results and puts it on arXiv right now, you lose potentially a lot. (Though not everything; if the result is reasonably deep posting your paper one or two days after the other group will result in recognition as "simultaneous discovery" at least.) 
If you posted your paper and someone else derived good applications from it, you still gain some increases in your h-index (probably). 
Posting things on arXiv does not mean the paper is immutable. You can continue to think about further applications and revise the paper as necessary. It is only after you submitted the paper at a journal for review that you really have to start worrying about making big changes to the manuscript. 


But absent you finding out exactly why it is that your co-author is reluctant to post the manuscript on arXiv, the brainstorming sessions with strangers on the internet can only go so far. 

I probably am not familiar with your subfield of mathematics, but this mentality of "In mathematics being able to apply your result is what makes it more sellable, papers are sometimes turned down if the result itself is too technical but there are no applications in sight" is foreign to me. In PDEs frequently a technique is developed to solve one or two problems initially. And the originators then work very hard the next few years to extend the technique to apply to many different problems. It is surprising that you are still worrying about the number of applications when you already have five!