5
votes
3answers
220 views

Isoperimetric inequality, isodiametric inequality, hyperplane conjecture… what are the inequalities of this kind known or conjectured?

Question: Which inequalities similar to the famous isoperimetric inequality is known? conjectured? I recently learned about some inequalities which are all similar to the famous isoperimetric ...
9
votes
4answers
993 views

recommending books for intro to diff. geometry

I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, stoke's thm, dRham chomology, ...
23
votes
10answers
4k views

“Immediate” Applications of Differential Geometry

My professor asked us to find and make a list of things/facts from real life which have a differential geometry interpretation or justification. One example is this older question of mine. Another ...
2
votes
4answers
1k views

Problems that differential geometry solves

Recently, I've been studying a course in differential geometry. Some keywords include (differentiable) manifold, atlas, (co)tangent space, vector field, integral curve, lie derivative, lie bracket, ...
3
votes
3answers
172 views

Motivating differentiable manifolds

I'm reading lectures for the first time starting next week ^_^ The subject is calculus on manifolds I was told that the students I'll be lecturing are not motivated (at all), so I need to kick off the ...