area minimizing
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2022 ◽  
Vol 359 (10) ◽  
pp. 1225-1232
Author(s):  
Fabiano G. B. Brito ◽  
Jackeline Conrado ◽  
Icaro Gonçalves ◽  
Adriana V. Nicoli

2021 ◽  
Vol 11 (22) ◽  
pp. 10739
Author(s):  
Mario Faenza ◽  
Giuseppina Piccolo ◽  
Mariano Funaro ◽  
Roberto Grella ◽  
Ilenia Pantano ◽  
...  

Giant cell arteritis (GCA) is a quite common panarteritis of the elderly that affects medium- and large-size arteries. Despite the increasing role of imaging with advancing technology, the gold standard for the diagnosis of GCA is still the temporal artery biopsy. A described complication of superficial temporal artery biopsy (STAB), for which incidence is not clear, is the accidental damage of the frontal branch of the facial nerve. In this paper, we described the short-scar facelift surgical approach for STAB on 23 consecutive patients who underwent unilateral superficial temporal artery biopsy for GCA suspicion. We collected data in terms of postoperative complications, biopsy specimen length, biopsy result and cosmetic appearance of the scar. In our experience, this surgical approach combines the advantage of avoiding incisions within the dangerous anatomical area, minimizing the risk of facial nerve damage, with an acceptable complication rate and a good final aesthetic result which avoids visible scarring.


Author(s):  
Ezequiel Barbosa ◽  
Franciele Conrado

In this work, we consider oriented compact manifolds which possess convex mean curvature boundary, positive scalar curvature and admit a map to $\mathbb {D}^{2}\times T^{n}$ with non-zero degree, where $\mathbb {D}^{2}$ is a disc and $T^{n}$ is an $n$ -dimensional torus. We prove the validity of an inequality involving a mean of the area and the length of the boundary of immersed discs whose boundaries are homotopically non-trivial curves. We also prove a rigidity result for the equality case when the boundary is strongly totally geodesic. This can be viewed as a partial generalization of a result due to Lucas Ambrózio in (2015, J. Geom. Anal., 25, 1001–1017) to higher dimensions.


2021 ◽  
Vol 280 (3) ◽  
pp. 108827
Author(s):  
Qiang Gao ◽  
Hengyu Zhou
Keyword(s):  

2021 ◽  
Vol 46 (2) ◽  
pp. 945-956 ◽  
Author(s):  
Sebastiano Nicolussi Golo ◽  
Manuel Ritoré

Author(s):  
Camillo De Lellis ◽  
Jonas Hirsch ◽  
Andrea Marchese ◽  
Salvatore Stuvard

2020 ◽  
Vol 63 (12) ◽  
pp. 2523-2552 ◽  
Author(s):  
Qiang Gao ◽  
Hengyu Zhou
Keyword(s):  

2020 ◽  
Vol 30 (5) ◽  
pp. 1224-1336
Author(s):  
Camillo De Lellis ◽  
Jonas Hirsch ◽  
Andrea Marchese ◽  
Salvatore Stuvard

AbstractWe establish a first general partial regularity theorem for area minimizing currents $${\mathrm{mod}}(p)$$ mod ( p ) , for every p, in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m-dimensional area minimizing current $${\mathrm{mod}}(p)$$ mod ( p ) cannot be larger than $$m-1$$ m - 1 . Additionally, we show that, when p is odd, the interior singular set is $$(m-1)$$ ( m - 1 ) -rectifiable with locally finite $$(m-1)$$ ( m - 1 ) -dimensional measure.


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