I won't recommend bring Sharpe's Investment, although it's a good book. After all it's just a relatively rigorous undergrad and MBA-level book. It's so big, don't waste your precious laggage space for it. And it's old, it won't be that expensive to get an used one in U.S.
Books you should bring to U.S. should be those, you'll use intensely in your study and it's much cheaper outside U.S.
Asset Pricing is a good one. Some other candidates..
Financial Theory and Corporate Policy 4th ed. by Copeland, Weston, and Shastri (A very good PhD-level intro for Corporate finance study, I don't thinks there is another up-to-date text.)
Options, Futures, and other Derivatives 6th ed. by Hull (Unless there is no Derivatives part in the qualify of your program, this one should be a basic reference in Dervatives for finance PhD students no matter research interest. There are some new better Derivative textbooks like McDonald's, but a dictionary like textbook should not be a problem for PhD students.)
Real Analysis 3rd ed. by Royden or a good Advanced Calculus text book e.g. Principles of Mathematical Analysis 3rd ed. by Rudin (Well, if you don't think you need to study Real Analysis, please at least get something from Advanced Calculus.. Mathematics textbooks is an good investment cause the re-sell price is good.)
As for econometric and econ books.. I think you should ask faculty about which book they will use, there are many good textbooks for these topics, buy the text you will definitely use in your class would be the most efficient way. At most bring a already read econometric textbool for quick reference if you've been exposed to econometric before.