**Background**

In my thesis I look at same problem from a couple of different angles. To state it roughly, in each chapter I use a different technique or area of mathematics to try and gain further insight into a hard case that was shown to have a "negative" result in the early 90s. I believe my main contribution is a few cute insights/tricks and building connections between a couple of different areas/problems in mathematics.

**Chopping it**

I think I have about about 4-5 publishable chapters in my thesis but they all consider *the same problem*.

> Do I send them all to the same journal and let them take their pick? or different journals? but then how do I choose how to send what chapter to which journal?

My topic is 'probabilistic' and I think my results are novel. Unfortunately, I don't really know where to submit. Some related problems and theory have previously appeared in the *Annals of Probability* and *Journal of Functional Analysis*. Although novel, I don't really know if my work is of that technical calibre though. What other journals should I consider? Should I post on ArXiv first?

My favourite result is a very short chapter where I derive some cute estimates for a special case by "bare hands" without any big machinery. It is totally non-standard estimate but shows a new type of question one might pose about my problem (and also other problems). The paper would only be about 8-10 pages long, is this worthy to submit?

**Timing**

I think my ideas have a lot of potential and would like to submit to a top journal, but due to timing constraints and working by myself, I still think my work is a bit "shallow". Ideally, I would like to have a good co-author to refine and deepen the ideas and turn it into a great publication but every time I mention my work to someone it seems like I  "inspire" them and shortly after they produce a paper with their co-authors on a similar or more abstract result. Very frustrating!

I need to submit my thesis in a month but haven't published my results yet. Some people are hot on my trail and I'm also worried that I might "inspire" my thesis referees. 

> Should I submit my chapters to journals before I receive my thesis referee reports back?

**Quality**

Due to my previous experiences, I'm only getting people that are not directly interested in my results to proof read (this includes my supervisor) but I'm a bit worried that they are only skimming over my thesis. 

> Should I be concerned?

Thanks in advance for your advice :)