I am a PhD student in mathematics. Recently, I could extend some old result to higher dimensional. I want to make a paper. But I doubt that is a good result or not, because most part of my proof is the same as the proof in the orginal version. In fact, what I did: I try to understand which part of the proof does not work for higher dimensional. So, I replace them by higher dimentioanl theorems. Do I neglect my result and do not make a paper? Or I have to do it?
I checked that no one did it before me.