HONG KONG—Hong Kong reported a record 34,466 new coronavirus infections Monday as deaths continued to climb, as authorities assess the possibilities of locking down the city. Hong Kong is grappling with a coronavirus surge driven primarily by the Omicron variant. Daily cases have more than quadrupled from a week ago, when the city reported over 7,500 infections. “Once every three days the case number will double,” said Albert Au, principal medical and health officer of the city’s Centre for Health Protection during a daily virus briefing. “We think that the number will continue to climb.” The city also reported 87 deaths Monday. Health authorities said the government could implement measures that may involve “asking people to stay at home,” and that it remains to be seen whether it would be done via legislation or other means. Hong Kong health minister Sophia Chan said during a radio program Monday that the …