Glen Wheeler
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 Sep3 comment Existence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$ I guess I was too subtle in my suggestion that the addition of a note to the effect of "The existence of a bijection is clear, it is the additional continuity hypothesis that is at work here." could improve the answer. Sep1 comment Existence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$ And if we drop the continuity hypothesis? Jun11 comment Generalization of ellipse equation to higher dimensional surfaces I would guess this is highly dependent on the magnitude of $c$ in relation to the width of the one-dimensional ellipse $e$. In particular, if $c$ is too small, $S$ is empty. Is this really what you want? Jun8 awarded Caucus Jun4 comment differential and arc length notation question @soup This is totally standard when we take as a measure something induced by the map we are studying. You can see this same computation coming up in the first variation of the area element. I'm not sure what you mean by transport theorem. May31 comment Usage of the word “formal(ly)” This is just an English language quirk. There are two basic meanings of 'formal' -- something related to 'form', which is not what you have in mind (despite being what Jazwinksi has in mind), and being rigorous. Mathematicians typically use the word rigorous when they mean rigorous. May31 answered evolution of curvature under ricci flow , What does the tensor A*B means? May30 answered differential and arc length notation question Mar23 comment Does every closed curve contain the vertices of a square? The question is essentially settled for $C^2$ curves, locally graphical curves if we restrict ourselves to one codimension. There is still more to be done (rectifiable curves would be interesting). Mar23 comment How to prove convex+concave=affine? @breezeintopl Click the green checkmark near the voting controls. Mar7 comment How to show given PDE preserves length while evolving curve to circle? @Willie Right, while I would say showing that length is preserved is elementary, showing the parabolic regularity and global existence is not. (The classification of the limit is likely again elementary, like you say.) Mar7 comment Where does the mass disappear in Fatou's Lemma? @Shyam I (personally) visualise a sequence of functions as being time-slices from some abstract energy-minimising evolution equation. Relaxation is just a synonym for taking a limit of these time-slices, and is a reduction of energy ('Excitation' being the opposite). Relaxation doesn't always give an equilibrium. In the sense it is used here, it is just a synonym for taking a limit. Mar7 answered How to show given PDE preserves length while evolving curve to circle? Mar7 answered Calabi flow and Robinson - Trautman equation Mar7 answered Where does the mass disappear in Fatou's Lemma? Feb10 accepted Nonlinear Fubini-Tonelli? Jan12 awarded Nice Question Dec2 awarded Yearling Sep2 awarded Revival Aug31 answered Calculating the area of a special hexagon