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Results tagged with geometric-analysis
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user 11260
6
votes
Accepted
Are there currently any plausible approaches to proving the Penrose сonjecture?
The difficulty of a general proof was discussed in A counter-example to a recent version of the Penrose conjecture (2010): a general existence theorem cannot be expected with boundary conditions compa …
- 188k
2
votes
The attractive 'force' between phase interfaces in the Allen-Cahn model
The gradient flow
$$\frac{\partial u}{\partial t}=\epsilon^2\Delta u+f(u),\;\;\text{with}\;\;f(u)=u(1-u^2),$$
of the Allen-Cahn functional has no inertia (there is no second order derivative in time), …
- 188k
9
votes
Is there a solution of the Yamabe problem using Ricci flow?
I presume you are referring to the Yamabe flow approach to the Yamabe problem, which in 2 dimensions reduces to a Ricci flow. Relevant references include
The
Ricci flow on surfaces (1988)
The Ricci
…
- 188k