Geometric Measure Theory and the Calculus of Variations

1986 ◽  
Keyword(s):  
Calculus Of Variations ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Geometric Measure

scholarly journals Nonexistence of stable currents in submanifolds of a product of two spheres

1991 ◽  
Vol 44 (2) ◽  
pp. 325-336 ◽  
Author(s):  
Xue-shan Zhang
Keyword(s):  
Calculus Of Variations ◽  
Homology Group ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Vanishing Theorems ◽  
Geometric Measure ◽  
Integral Currents

By using techniques of the calculus of variations in geometric measure theory, we investigate the nonexistence of stable integral currents in Sn1 × Sn2 and its immersed submanifolds. Several vanishing theorems concerning the homology group of these manifolds are established.

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