Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perelman's functionals on cones and Construction of type III Ricci flows
  coming out of cones   In this paper, we are interested in conical structures of manifolds with
respect to the Ricci flow and, in particular, we study them from the point of
view of Perelman's functionals.
  In a first part, we study Perelman's $\lambda$ and $\nu$ functionals of cones
and characterize their finiteness in terms of the $\lambda$-functional of the
link. As an application, we characterize manifolds with conical singularities
on which a $\lambda$-functional can be defined and get upper bounds on the
$\nu$-functional of asymptotically conical manifolds.
  We then present an adaptation of the proof of Perelman's pseudolocality
theorem and prove that cones over some perturbations of the unit sphere can be
smoothed out by type III immortal solutions on the Ricci flow.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org