scholarly journals Singularities Of Energy-Minimizing Maps From The Ball To The Sphere

Inequalities ◽  
2002 ◽  
pp. 637-639
Author(s):  
Frederick J. Almgren ◽  
Elliott H. Lieb
Keyword(s):  
Minimizing Maps

scholarly journals A Lioville Type Theorem for Minimizing Maps

2002 ◽  
Vol 9 (3) ◽  
pp. 407-424 ◽  
Author(s):  
Fengbo Hang ◽  
Fanghua Lin
Keyword(s):  
Type Theorem ◽  
Minimizing Maps

Regularity ofp-energy minimizing maps andp-superstrongly unstable indices

1994 ◽  
Vol 4 (2) ◽  
pp. 247-272 ◽  
Author(s):  
S. Walter Wei ◽  
Chi-Ming Yau
Keyword(s):  
Minimizing Maps

scholarly journals Quantitative Regularity for p-Minimizing Maps Through a Reifenberg Theorem

2021 ◽  
Author(s):  
Mattia Vedovato
Keyword(s):  
Riemannian Manifolds ◽  
Upper Bound ◽  
Type Theorem ◽  
Regularity Result ◽  
Singular Points ◽  
Singular Set ◽  
Minkowski Content ◽  
Minimizing Maps ◽  
Quantitative Regularity ◽  
Appl Math

AbstractIn this article we extend to arbitrary p-energy minimizing maps between Riemannian manifolds a regularity result which is known to hold in the case $$p=2$$ p = 2 . We first show that the set of singular points of such a map can be quantitatively stratified: we classify singular points based on the number of almost-symmetries of the map around them, as done in Cheeger and Naber (Commun Pure Appl Math 66(6): 965–990, 2013). Then, adapting the work of Naber and Valtorta (Ann Math (2) 185(1): 131–227, 2017), we apply a Reifenberg-type Theorem to each quantitative stratum; through this, we achieve an upper bound on the Minkowski content of the singular set, and we prove it is k-rectifiable for a k which only depends on p and the dimension of the domain.

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