Mountain View, Calif. IN late December, Marissa Mayer was vacationing in Africa when her boss, Jonathan Rosenberg, e-mailed her asking if she was leaving Google. It wasn’t a routine query. As the gatekeeper of Google’s home page, and one of the company’s most ubiquitous and closely watched public faces, Ms. Mayer controls the look, feel and functionality of the Internet’s most heavily trafficked s