Coco Gauff has been proclaimed the heir to the Williams sisters ever since she defeated Venus at Wimbledon, a comparison that she resisted, even as she acknowledged the honor. She ranks at a career-high No. 11 in singles; in doubles, as of this month, she is the No. 1 player in the world. Gauff has the benefit of millions of dollars in endorsements and prize money and a signature sneaker from New Balance — but as she heads to the U.S. Open, which starts on Aug. 29, she is still only 18, a precarious age when many young people toggle between a sense of invincibility and utter insecurity. The weight of what she carries would be a lot for anyone, but maybe especially for a young woman like Gauff; she knows from personal experience that so many girls are watching her. Many are looking to Gauff — a young player who offers the excitement of potential along with exceptional athleticism and an ease with the public — to be the new face of American tennis, to be an inspiring figure even for young people who never pick up a racket. But before Coco Gauff can fully realize her own dreams or anyone else’s, Gauff has to do one thing she has not yet accomplished at the highest level: She has to win. Photograph by @ariellebobbwillis.