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We discuss the concepts of energy and mass in relativity. On a finitelyextended spatial region, they lead to the notion of quasilocal energy/mass forthe boundary 2-surface in spacetime. A new definition was found in [27] thatsatisfies the positivity, rigidity, and asymptotics properties. The definitionmakes use of the surface Hamiltonian term which arises from Hamilton-Jacobianalysis of the gravitation action. The reference surface Hamiltonian isassociated with an isometric embedding of the 2-surface into the Minkowskispace. We discuss this new definition of mass as well as the reference sur-face Hamiltonian. Most of the discussion is based on joint work with PoNingChen and Shing-Tung Yau.

Quasilocal mass and surface Hamiltonian in spacetime