In this paper, we show how under the continuum hypothesis one can obtain an integral representation for elements of the topological dual of the space of functions of bounded variation in terms of Lebesgue and Kolmogorov-Burkill integrals.

This talk will give a very brief outline how a portion of geometric analysis was carried out in relation to geometry, nonlinear partial differential equations and mathematical physics. My personal experience is that this is a beautiful subject with great depth and it touches almost all branch of mathematics.

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We show that the recently proposed weak gravity conjecture\cite{AMNV0601} can be extended to a class of scalar field theories. Taking gravity into account, we find an upper bound on the gravity interaction strength, expressed in terms of scalar coupling parameters. This conjecture is supported by some two-dimensional models and noncommutative field theories.

No abstract uploaded!